diff --git a/CHANGELOG.md b/CHANGELOG.md
index d135720aa1e..4753c8df0ce 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -6,6 +6,12 @@ This project adheres to [Semantic Versioning](http://semver.org/).
 
 ### Added
 
+- For `add_trace`, `add_shape`, `add_annotation` and `add_layout_image`, the `row` and/or `col` argument now also accept the string `"all"`. `row="all"` adds the object to all the subplot rows and `col="all"` adds the object to all the subplot columns.
+
+- Shapes that reference the plot axes in one dimension and the data in another dimension can be added with the new `add_hline`, `add_vline`, `add_hrect`, `add_vrect` functions, which also support the `row="all"` and `col="all"` arguments.
+
+- The `add_trace`, `add_shape`, `add_annotation`, `add_layout_image`, `add_hline`, `add_vline`, `add_hrect`, `add_vrect` functions accept an argument `exclude_empty_subplots` which if `True`, only adds the object to subplots already containing traces or layout objects. This is useful in conjunction with the `row="all"` and `col="all"` arguments.
+
 - For all `go.Figure` functions accepting a selector argument (e.g., `select_traces`), this argument can now also be a function which is passed each relevant graph object (in the case of `select_traces`, it is passed every trace in the figure). For graph objects where this function returns true, the graph object is included in the selection.
 
 ### Updated
diff --git a/packages/python/plotly/plotly/basedatatypes.py b/packages/python/plotly/plotly/basedatatypes.py
index 8cb0b07a05d..f2033cf359a 100644
--- a/packages/python/plotly/plotly/basedatatypes.py
+++ b/packages/python/plotly/plotly/basedatatypes.py
@@ -1302,7 +1302,9 @@ def _add_annotation_like(
             # if exclude_empty_subplots is True, check to see if subplot is
             # empty and return if it is
             if exclude_empty_subplots and (
-                not self._subplot_contains_trace(xref, yref)
+                not self._subplot_not_empty(
+                    xref, yref, selector=bool(exclude_empty_subplots)
+                )
             ):
                 return self
             # in case the user specified they wanted an axis to refer to the
@@ -1993,8 +1995,8 @@ def add_traces(
         if exclude_empty_subplots:
             data = list(
                 filter(
-                    lambda trace: self._subplot_contains_trace(
-                        trace["xaxis"], trace["yaxis"]
+                    lambda trace: self._subplot_not_empty(
+                        trace["xaxis"], trace["yaxis"], bool(exclude_empty_subplots)
                     ),
                     data,
                 )
@@ -3873,19 +3875,56 @@ def _has_subplots(self):
         single plot and so this returns False. """
         return self._grid_ref is not None
 
-    def _subplot_contains_trace(self, xref, yref):
-        return any(
-            t == (xref, yref)
-            for t in [
-                # if a trace exists but has no xaxis or yaxis keys, then it
-                # is plotted with xaxis 'x' and yaxis 'y'
-                (
-                    "x" if d["xaxis"] is None else d["xaxis"],
-                    "y" if d["yaxis"] is None else d["yaxis"],
+    def _subplot_not_empty(self, xref, yref, selector="all"):
+        """
+        xref: string representing the axis. Objects in the plot will be checked
+              for this xref (for layout objects) or xaxis (for traces) to
+              determine if they lie in a certain subplot.
+        yref: string representing the axis. Objects in the plot will be checked
+              for this yref (for layout objects) or yaxis (for traces) to
+              determine if they lie in a certain subplot.
+        selector: can be "all" or an iterable containing some combination of
+                  "traces", "shapes", "annotations", "images". Only the presence
+                  of objects specified in selector will be checked. So if
+                  ["traces","shapes"] is passed then a plot we be considered
+                  non-empty if it contains traces or shapes. If
+                  bool(selector) returns False, no checking is performed and
+                  this function returns True. If selector is True, it is
+                  converted to "all".
+        """
+        if not selector:
+            # If nothing to select was specified then a subplot is always deemed non-empty
+            return True
+        if selector == True:
+            selector = "all"
+        if selector == "all":
+            selector = ["traces", "shapes", "annotations", "images"]
+        ret = False
+        for s in selector:
+            if s == "traces":
+                obj = self.data
+                xaxiskw = "xaxis"
+                yaxiskw = "yaxis"
+            elif s in ["shapes", "annotations", "images"]:
+                obj = self.layout[s]
+                xaxiskw = "xref"
+                yaxiskw = "yref"
+            else:
+                obj = None
+            if obj:
+                ret |= any(
+                    t == (xref, yref)
+                    for t in [
+                        # if a object exists but has no xaxis or yaxis keys, then it
+                        # is plotted with xaxis/xref 'x' and yaxis/yref 'y'
+                        (
+                            "x" if d[xaxiskw] is None else d[xaxiskw],
+                            "y" if d[yaxiskw] is None else d[yaxiskw],
+                        )
+                        for d in obj
+                    ]
                 )
-                for d in self.data
-            ]
-        )
+        return ret
 
 
 class BasePlotlyType(object):
diff --git a/packages/python/plotly/plotly/tests/test_core/test_figure_messages/test_add_traces.py b/packages/python/plotly/plotly/tests/test_core/test_figure_messages/test_add_traces.py
index 5563a419732..63f379bbcd8 100644
--- a/packages/python/plotly/plotly/tests/test_core/test_figure_messages/test_add_traces.py
+++ b/packages/python/plotly/plotly/tests/test_core/test_figure_messages/test_add_traces.py
@@ -120,7 +120,43 @@ def test_add_trace_no_exclude_empty_subplots():
     fig.add_trace(go.Scatter(x=[1, 2, 3], y=[5, 1, 2]), row=1, col=1)
     fig.add_trace(go.Scatter(x=[1, 2, 3], y=[2, 1, -7]), row=2, col=2)
     # Add traces with exclude_empty_subplots set to true and make sure this
-    # doesn't add to traces that don't already have data
+    # even adds to traces that don't already have data
+    fig.add_trace(go.Scatter(x=[1, 2, 3], y=[0, 1, -1]), row="all", col="all")
+    assert len(fig.data) == 6
+    assert fig.data[2]["xaxis"] == "x" and fig.data[2]["yaxis"] == "y"
+    assert fig.data[3]["xaxis"] == "x2" and fig.data[3]["yaxis"] == "y2"
+    assert fig.data[4]["xaxis"] == "x3" and fig.data[4]["yaxis"] == "y3"
+    assert fig.data[5]["xaxis"] == "x4" and fig.data[5]["yaxis"] == "y4"
+
+
+def test_add_trace_exclude_totally_empty_subplots():
+    # Add traces
+    fig = make_subplots(2, 2)
+    fig.add_trace(go.Scatter(x=[1, 2, 3], y=[5, 1, 2]), row=1, col=1)
+    fig.add_trace(go.Scatter(x=[1, 2, 3], y=[2, 1, -7]), row=2, col=2)
+    fig.add_shape(dict(type="rect", x0=0, x1=1, y0=0, y1=1), row=1, col=2)
+    # Add traces with exclude_empty_subplots set to true and make sure this
+    # doesn't add to traces that don't already have data or layout objects
+    fig.add_trace(
+        go.Scatter(x=[1, 2, 3], y=[0, 1, -1]),
+        row="all",
+        col="all",
+        exclude_empty_subplots=["anything", "truthy"],
+    )
+    assert len(fig.data) == 5
+    assert fig.data[2]["xaxis"] == "x" and fig.data[2]["yaxis"] == "y"
+    assert fig.data[3]["xaxis"] == "x2" and fig.data[3]["yaxis"] == "y2"
+    assert fig.data[4]["xaxis"] == "x4" and fig.data[4]["yaxis"] == "y4"
+
+
+def test_add_trace_no_exclude_totally_empty_subplots():
+    # Add traces
+    fig = make_subplots(2, 2)
+    fig.add_trace(go.Scatter(x=[1, 2, 3], y=[5, 1, 2]), row=1, col=1)
+    fig.add_trace(go.Scatter(x=[1, 2, 3], y=[2, 1, -7]), row=2, col=2)
+    fig.add_shape(dict(type="rect", x0=0, x1=1, y0=0, y1=1), row=1, col=2)
+    # Add traces with exclude_empty_subplots set to true and make sure this
+    # even adds to traces that don't already have data or layout objects
     fig.add_trace(go.Scatter(x=[1, 2, 3], y=[0, 1, -1]), row="all", col="all")
     assert len(fig.data) == 6
     assert fig.data[2]["xaxis"] == "x" and fig.data[2]["yaxis"] == "y"
diff --git a/packages/python/plotly/plotly/tests/test_core/test_subplots/test_find_nonempty_subplots.py b/packages/python/plotly/plotly/tests/test_core/test_subplots/test_find_nonempty_subplots.py
new file mode 100644
index 00000000000..27a66b4feea
--- /dev/null
+++ b/packages/python/plotly/plotly/tests/test_core/test_subplots/test_find_nonempty_subplots.py
@@ -0,0 +1,61 @@
+import pytest
+import plotly.graph_objects as go
+from plotly.subplots import make_subplots
+from itertools import combinations, product
+from functools import reduce
+
+
+def all_combos(it):
+    return list(
+        reduce(
+            lambda a, b: a + b,
+            [list(combinations(it, r)) for r in range(1, len(it))],
+            [],
+        )
+    )
+
+
+def translate_layout_keys(t):
+    xr, yr = t
+    xr = xr.replace("axis", "")
+    yr = yr.replace("axis", "")
+    return (xr, yr)
+
+
+def get_non_empty_subplots(fig, selector):
+    gr = fig._validate_get_grid_ref()
+    nrows = len(gr)
+    ncols = len(gr[0])
+    sp_addresses = product(range(nrows), range(ncols))
+    # assign a number similar to plotly's xref/yref (e.g, xref=x2) to each
+    # subplot address (xref=x -> 1, but xref=x3 -> 3)
+    # sp_ax_numbers=range(1,len(sp_addresses)+1)
+    # Get those subplot numbers which contain something
+    ret = list(
+        filter(
+            lambda sp: fig._subplot_not_empty(
+                *translate_layout_keys(sp.layout_keys), selector=selector
+            ),
+            [gr[r][c][0] for r, c in sp_addresses],
+        )
+    )
+    return ret
+
+
+def test_choose_correct_non_empty_subplots():
+    # This checks to see that the correct subplots are selected for all
+    # combinations of selectors
+    fig = make_subplots(2, 2)
+    fig.add_trace(go.Scatter(x=[1, 2], y=[3, 4]), row=1, col=1)
+    fig.add_shape(dict(type="rect", x0=1, x1=2, y0=3, y1=4), row=1, col=2)
+    fig.add_annotation(dict(text="A", x=1, y=2), row=2, col=1)
+    fig.add_layout_image(
+        dict(source="test", x=1, y=2, sizex=0.5, sizey=0.5), row=2, col=2
+    )
+    all_subplots = get_non_empty_subplots(fig, "all")
+    selectors = all_combos(["traces", "shapes", "annotations", "images"])
+    subplot_combos = all_combos(all_subplots)
+    assert len(selectors) == len(subplot_combos)
+    for s, spc in zip(selectors, subplot_combos):
+        sps = tuple(get_non_empty_subplots(fig, s))
+        assert sps == spc
diff --git a/packages/python/plotly/plotly/tests/test_core/test_update_objects/test_update_annotations.py b/packages/python/plotly/plotly/tests/test_core/test_update_objects/test_update_annotations.py
index c08129bb31b..e7ac974d68a 100644
--- a/packages/python/plotly/plotly/tests/test_core/test_update_objects/test_update_annotations.py
+++ b/packages/python/plotly/plotly/tests/test_core/test_update_objects/test_update_annotations.py
@@ -270,51 +270,78 @@ def test_image_attributes(self):
 
 
 def test_exclude_empty_subplots():
-    for k, fun, d in [
+    for k, fun, d, fun2, d2 in [
         (
             "shapes",
             go.Figure.add_shape,
             dict(type="rect", x0=1.5, x1=2.5, y0=3.5, y1=4.5),
+            # add a different type to make the check easier (otherwise we might
+            # mix up the objects added before and after fun was run)
+            go.Figure.add_annotation,
+            dict(x=1, y=2, text="A"),
+        ),
+        (
+            "annotations",
+            go.Figure.add_annotation,
+            dict(x=1, y=2, text="A"),
+            go.Figure.add_layout_image,
+            dict(x=3, y=4, sizex=2, sizey=3, source="test"),
         ),
-        ("annotations", go.Figure.add_annotation, dict(x=1, y=2, text="A")),
         (
             "images",
             go.Figure.add_layout_image,
             dict(x=3, y=4, sizex=2, sizey=3, source="test"),
+            go.Figure.add_shape,
+            dict(type="rect", x0=1.5, x1=2.5, y0=3.5, y1=4.5),
         ),
     ]:
         # make a figure where not all the subplots are populated
         fig = make_subplots(2, 2)
         fig.add_trace(go.Scatter(x=[1, 2, 3], y=[5, 1, 2]), row=1, col=1)
         fig.add_trace(go.Scatter(x=[1, 2, 3], y=[2, 1, -7]), row=2, col=2)
+        fun2(fig, d2, row=1, col=2)
         # add a thing to all subplots but make sure it only goes on the
-        # plots without data
-        fun(fig, d, row="all", col="all", exclude_empty_subplots=True)
-        assert len(fig.layout[k]) == 2
+        # plots without data or layout objects
+        fun(fig, d, row="all", col="all", exclude_empty_subplots="anything_truthy")
+        assert len(fig.layout[k]) == 3
         assert fig.layout[k][0]["xref"] == "x" and fig.layout[k][0]["yref"] == "y"
-        assert fig.layout[k][1]["xref"] == "x4" and fig.layout[k][1]["yref"] == "y4"
+        assert fig.layout[k][1]["xref"] == "x2" and fig.layout[k][1]["yref"] == "y2"
+        assert fig.layout[k][2]["xref"] == "x4" and fig.layout[k][2]["yref"] == "y4"
 
 
 def test_no_exclude_empty_subplots():
-    for k, fun, d in [
+    for k, fun, d, fun2, d2 in [
         (
             "shapes",
             go.Figure.add_shape,
             dict(type="rect", x0=1.5, x1=2.5, y0=3.5, y1=4.5),
+            # add a different type to make the check easier (otherwise we might
+            # mix up the objects added before and after fun was run)
+            go.Figure.add_annotation,
+            dict(x=1, y=2, text="A"),
+        ),
+        (
+            "annotations",
+            go.Figure.add_annotation,
+            dict(x=1, y=2, text="A"),
+            go.Figure.add_layout_image,
+            dict(x=3, y=4, sizex=2, sizey=3, source="test"),
         ),
-        ("annotations", go.Figure.add_annotation, dict(x=1, y=2, text="A")),
         (
             "images",
             go.Figure.add_layout_image,
             dict(x=3, y=4, sizex=2, sizey=3, source="test"),
+            go.Figure.add_shape,
+            dict(type="rect", x0=1.5, x1=2.5, y0=3.5, y1=4.5),
         ),
     ]:
         # make a figure where not all the subplots are populated
         fig = make_subplots(2, 2)
         fig.add_trace(go.Scatter(x=[1, 2, 3], y=[5, 1, 2]), row=1, col=1)
         fig.add_trace(go.Scatter(x=[1, 2, 3], y=[2, 1, -7]), row=2, col=2)
-        # add a thing to all subplots and make sure it even goes on the
-        # plots without data
+        fun2(fig, d2, row=1, col=2)
+        # add a thing to all subplots but make sure it only goes on the
+        # plots without data or layout objects
         fun(fig, d, row="all", col="all", exclude_empty_subplots=False)
         assert len(fig.layout[k]) == 4
         assert fig.layout[k][0]["xref"] == "x" and fig.layout[k][0]["yref"] == "y"