diff --git a/spacy/displacy/render.py b/spacy/displacy/render.py
index 2ab41ccc2..40b9986e8 100644
--- a/spacy/displacy/render.py
+++ b/spacy/displacy/render.py
@@ -142,7 +142,25 @@ class SpanRenderer:
         spans (list): Individual entity spans and their start, end, label, kb_id and kb_url.
         title (str / None): Document title set in Doc.user_data['title'].
         """
-        per_token_info = []
+        per_token_info = self._assemble_per_token_info(tokens, spans)
+        markup = self._render_markup(per_token_info)
+        markup = TPL_SPANS.format(content=markup, dir=self.direction)
+        if title:
+            markup = TPL_TITLE.format(title=title) + markup
+        return markup
+
+    @staticmethod
+    def _assemble_per_token_info(
+        tokens: List[str], spans: List[Dict[str, Any]]
+    ) -> List[Dict[str, List[Dict[str, Any]]]]:
+        """Assembles token info used to generate markup in render_spans().
+        tokens (List[str]): Tokens in text.
+        spans (List[Dict[str, Any]]): Spans in text.
+        RETURNS (List[Dict[str, List[Dict, str, Any]]]): Per token info needed to render HTML markup for given tokens
+            and spans.
+        """
+        per_token_info: List[Dict[str, List[Dict[str, Any]]]] = []
+
         # we must sort so that we can correctly describe when spans need to "stack"
         # which is determined by their start token, then span length (longer spans on top),
         # then break any remaining ties with the span label
@@ -154,21 +172,22 @@ class SpanRenderer:
                 s["label"],
             ),
         )
+
         for s in spans:
             # this is the vertical 'slot' that the span will be rendered in
             # vertical_position = span_label_offset + (offset_step * (slot - 1))
             s["render_slot"] = 0
+
         for idx, token in enumerate(tokens):
             # Identify if a token belongs to a Span (and which) and if it's a
             # start token of said Span. We'll use this for the final HTML render
             token_markup: Dict[str, Any] = {}
             token_markup["text"] = token
-            concurrent_spans = 0
+            intersecting_spans: List[Dict[str, Any]] = []
             entities = []
             for span in spans:
                 ent = {}
                 if span["start_token"] <= idx < span["end_token"]:
-                    concurrent_spans += 1
                     span_start = idx == span["start_token"]
                     ent["label"] = span["label"]
                     ent["is_start"] = span_start
@@ -176,7 +195,12 @@ class SpanRenderer:
                         # When the span starts, we need to know how many other
                         # spans are on the 'span stack' and will be rendered.
                         # This value becomes the vertical render slot for this entire span
-                        span["render_slot"] = concurrent_spans
+                        span["render_slot"] = (
+                            intersecting_spans[-1]["render_slot"]
+                            if len(intersecting_spans)
+                            else 0
+                        ) + 1
+                    intersecting_spans.append(span)
                     ent["render_slot"] = span["render_slot"]
                     kb_id = span.get("kb_id", "")
                     kb_url = span.get("kb_url", "#")
@@ -193,11 +217,8 @@ class SpanRenderer:
                     span["render_slot"] = 0
             token_markup["entities"] = entities
             per_token_info.append(token_markup)
-        markup = self._render_markup(per_token_info)
-        markup = TPL_SPANS.format(content=markup, dir=self.direction)
-        if title:
-            markup = TPL_TITLE.format(title=title) + markup
-        return markup
+
+        return per_token_info
 
     def _render_markup(self, per_token_info: List[Dict[str, Any]]) -> str:
         """Render the markup from per-token information"""
diff --git a/spacy/tests/test_displacy.py b/spacy/tests/test_displacy.py
index 12d903dca..b83c7db07 100644
--- a/spacy/tests/test_displacy.py
+++ b/spacy/tests/test_displacy.py
@@ -2,7 +2,7 @@ import numpy
 import pytest
 
 from spacy import displacy
-from spacy.displacy.render import DependencyRenderer, EntityRenderer
+from spacy.displacy.render import DependencyRenderer, EntityRenderer, SpanRenderer
 from spacy.lang.en import English
 from spacy.lang.fa import Persian
 from spacy.tokens import Doc, Span
@@ -468,3 +468,23 @@ def test_issue12816(en_vocab) -> None:
     # Verify that the HTML tag is still escaped
     html = displacy.render(doc, style="span")
     assert "&lt;TEST&gt;" in html
+
+
+@pytest.mark.issue(13056)
+def test_displacy_span_stacking():
+    """Test whether span stacking works properly for multiple overlapping spans."""
+    spans = [
+        {"start_token": 2, "end_token": 5, "label": "SkillNC"},
+        {"start_token": 0, "end_token": 2, "label": "Skill"},
+        {"start_token": 1, "end_token": 3, "label": "Skill"},
+    ]
+    tokens = ["Welcome", "to", "the", "Bank", "of", "China", "."]
+    per_token_info = SpanRenderer._assemble_per_token_info(spans=spans, tokens=tokens)
+
+    assert len(per_token_info) == len(tokens)
+    assert all([len(per_token_info[i]["entities"]) == 1 for i in (0, 3, 4)])
+    assert all([len(per_token_info[i]["entities"]) == 2 for i in (1, 2)])
+    assert per_token_info[1]["entities"][0]["render_slot"] == 1
+    assert per_token_info[1]["entities"][1]["render_slot"] == 2
+    assert per_token_info[2]["entities"][0]["render_slot"] == 2
+    assert per_token_info[2]["entities"][1]["render_slot"] == 3