diff --git a/doc/users/next_whats_new/errorbar_offsets.rst b/doc/users/next_whats_new/errorbar_offsets.rst
new file mode 100644
index 000000000000..b2ca9f7a23c5
--- /dev/null
+++ b/doc/users/next_whats_new/errorbar_offsets.rst
@@ -0,0 +1,10 @@
+Errorbar plots can shift which points have error bars
+-----------------------------------------------------
+
+Previously, `plt.errorbar()` accepted a kwarg `errorevery` such that the
+command `plt.errorbar(x, y, yerr, errorevery=6)` would add error bars to
+datapoints `x[::6], y[::6]`.
+
+`errorbar()` now also accepts a tuple for `errorevery` such that
+`plt.errorbar(x, y, yerr, errorevery=(start, N))` adds error bars to points
+`x[start::N], y[start::N]`.
diff --git a/examples/lines_bars_and_markers/errorbar_subsample.py b/examples/lines_bars_and_markers/errorbar_subsample.py
index 8b4d11087ac7..a54c66cf5655 100644
--- a/examples/lines_bars_and_markers/errorbar_subsample.py
+++ b/examples/lines_bars_and_markers/errorbar_subsample.py
@@ -12,23 +12,29 @@
 
 # example data
 x = np.arange(0.1, 4, 0.1)
-y = np.exp(-x)
+y1 = np.exp(-1.0 * x)
+y2 = np.exp(-0.5 * x)
 
 # example variable error bar values
-yerr = 0.1 + 0.1 * np.sqrt(x)
+y1err = 0.1 + 0.1 * np.sqrt(x)
+y2err = 0.1 + 0.1 * np.sqrt(x/2)
 
 
 # Now switch to a more OO interface to exercise more features.
-fig, axs = plt.subplots(nrows=1, ncols=2, sharex=True)
-ax = axs[0]
-ax.errorbar(x, y, yerr=yerr)
-ax.set_title('all errorbars')
+fig, (ax_l, ax_c, ax_r) = plt.subplots(nrows=1, ncols=3,
+                                       sharex=True, figsize=(12, 6))
 
-ax = axs[1]
-ax.errorbar(x, y, yerr=yerr, errorevery=5)
-ax.set_title('only every 5th errorbar')
+ax_l.set_title('all errorbars')
+ax_l.errorbar(x, y1, yerr=y1err)
+ax_l.errorbar(x, y2, yerr=y2err)
 
+ax_c.set_title('only every 6th errorbar')
+ax_c.errorbar(x, y1, yerr=y1err, errorevery=6)
+ax_c.errorbar(x, y2, yerr=y2err, errorevery=6)
 
-fig.suptitle('Errorbar subsampling for better appearance')
+ax_r.set_title('second series shifted by 3')
+ax_r.errorbar(x, y1, yerr=y1err, errorevery=(0, 6))
+ax_r.errorbar(x, y2, yerr=y2err, errorevery=(3, 6))
 
+fig.suptitle('Errorbar subsampling for better appearance')
 plt.show()
diff --git a/lib/matplotlib/axes/_axes.py b/lib/matplotlib/axes/_axes.py
index c7ad1a61fc8d..8257bb4dcd70 100644
--- a/lib/matplotlib/axes/_axes.py
+++ b/lib/matplotlib/axes/_axes.py
@@ -3143,10 +3143,14 @@ def errorbar(self, x, y, yerr=None, xerr=None,
             and *yerr*.  To use limits with inverted axes, :meth:`set_xlim`
             or :meth:`set_ylim` must be called before :meth:`errorbar`.
 
-        errorevery : positive integer, optional, default: 1
-            Subsamples the errorbars. e.g., if errorevery=5, errorbars for
-            every 5-th datapoint will be plotted. The data plot itself still
-            shows all data points.
+        errorevery : int or (int, int), optional, default: 1
+            draws error bars on a subset of the data. *errorevery* =N draws
+            error bars on the points (x[::N], y[::N]).
+            *errorevery* =(start, N) draws error bars on the points
+            (x[start::N], y[start::N]). e.g. errorevery=(6, 3)
+            adds error bars to the data at (x[6], x[9], x[12], x[15], ...).
+            Used to avoid overlapping error bars when two series share x-axis
+            values.
 
         Returns
         -------
@@ -3191,9 +3195,17 @@ def errorbar(self, x, y, yerr=None, xerr=None,
         kwargs = {k: v for k, v in kwargs.items() if v is not None}
         kwargs.setdefault('zorder', 2)
 
-        if errorevery < 1:
+        try:
+            offset, errorevery = errorevery
+        except TypeError:
+            offset = 0
+
+        if errorevery < 1 or int(errorevery) != errorevery:
+            raise ValueError(
+                'errorevery must be positive integer or tuple of integers')
+        if int(offset) != offset:
             raise ValueError(
-                'errorevery has to be a strictly positive integer')
+                'errorevery\'s starting index must be an integer')
 
         self._process_unit_info(xdata=x, ydata=y, kwargs=kwargs)
 
@@ -3302,7 +3314,8 @@ def errorbar(self, x, y, yerr=None, xerr=None,
         xlolims = np.broadcast_to(xlolims, len(x)).astype(bool)
         xuplims = np.broadcast_to(xuplims, len(x)).astype(bool)
 
-        everymask = np.arange(len(x)) % errorevery == 0
+        everymask = np.zeros(len(x), bool)
+        everymask[offset::errorevery] = True
 
         def xywhere(xs, ys, mask):
             """
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index 9f8e2ce60e24..ea45561d6599 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -2945,6 +2945,29 @@ def test_errorbar_with_prop_cycle():
     ax.errorbar(x=[2, 4, 10], y=[6, 4, 2], yerr=0.5)
 
 
+@check_figures_equal()
+def test_errorbar_offsets(fig_test, fig_ref):
+    x = np.linspace(0, 1, 15)
+    y = x * (1-x)
+    yerr = y/6
+
+    ax_ref = fig_ref.subplots()
+    ax_test = fig_test.subplots()
+
+    for color, shift in zip('rgbk', [0, 0, 2, 7]):
+        y += .02
+
+        # Using feature in question
+        ax_test.errorbar(x, y, yerr, errorevery=(shift, 4),
+                         capsize=4, c=color)
+
+        # Using manual errorbars
+        # n.b. errorbar draws the main plot at z=2.1 by default
+        ax_ref.plot(x, y, c=color, zorder=2.1)
+        ax_ref.errorbar(x[shift::4], y[shift::4], yerr[shift::4],
+                        capsize=4, c=color, fmt='none')
+
+
 @image_comparison(baseline_images=['hist_stacked_stepfilled',
                                    'hist_stacked_stepfilled'])
 def test_hist_stacked_stepfilled():