diff --git a/spec/fixtures/expected-schema-from-draft-04-to-07.json b/spec/fixtures/expected-schema-from-draft-04-to-07.json
index abad5e1..6ba8249 100644
--- a/spec/fixtures/expected-schema-from-draft-04-to-07.json
+++ b/spec/fixtures/expected-schema-from-draft-04-to-07.json
@@ -9,6 +9,30 @@
     "num": {
       "$id": "another-schema#num",
       "type": "string"
+    },
+    "exclusiveMaximum": {
+      "$ref": "http://json-schema.org/draft-07/schema#/properties/exclusiveMaximum"
+    },
+    "maxLength": {
+      "$ref": "http://json-schema.org/draft-07/schema#/definitions/nonNegativeInteger"
+    },
+    "parametersList": {
+      "type": "array",
+      "description": "The parameters needed to send a valid API call.",
+      "additionalItems": false,
+      "items": [
+        {
+          "oneOf": [
+            {
+              "$ref": "#/definitions/parameter"
+            },
+            {
+              "$ref": "#/definitions/jsonReference"
+            }
+          ]
+        }
+      ],
+      "uniqueItems": true
     }
   },
   "properties": {
@@ -20,6 +44,12 @@
       "minimum": 1,
       "maximum": 3
     },
+    "exclusiveMaximum": {
+      "$ref": "#/definitions/exclusiveMaximum"
+    },
+    "maxLength": {
+      "$ref": "#/definitions/maxLength"
+    },
     "singleValue": {"const": "foo"},
     "singleValueConstant": {"const": "foo"},
     "multipleValues": {"enum": ["foo", "bar"]},
diff --git a/spec/fixtures/expected-schema-from-draft-04-to-2019.json b/spec/fixtures/expected-schema-from-draft-04-to-2019.json
index 619cc6c..e626eb5 100644
--- a/spec/fixtures/expected-schema-from-draft-04-to-2019.json
+++ b/spec/fixtures/expected-schema-from-draft-04-to-2019.json
@@ -10,6 +10,30 @@
       "$id": "another-schema",
       "$anchor": "num",
       "type": "string"
+    },
+    "exclusiveMaximum": {
+      "$ref": "http://json-schema.org/draft-07/schema#/properties/exclusiveMaximum"
+    },
+    "maxLength": {
+      "$ref": "http://json-schema.org/draft-07/schema#/definitions/nonNegativeInteger"
+    },
+    "parametersList": {
+      "type": "array",
+      "description": "The parameters needed to send a valid API call.",
+      "additionalItems": false,
+      "items": [
+        {
+          "oneOf": [
+            {
+              "$ref": "#/definitions/parameter"
+            },
+            {
+              "$ref": "#/definitions/jsonReference"
+            }
+          ]
+        }
+      ],
+      "uniqueItems": true
     }
   },
   "properties": {
@@ -21,6 +45,12 @@
       "minimum": 1,
       "maximum": 3
     },
+    "exclusiveMaximum": {
+      "$ref": "#/definitions/exclusiveMaximum"
+    },
+    "maxLength": {
+      "$ref": "#/definitions/maxLength"
+    },
     "singleValue": {"const": "foo"},
     "singleValueConstant": {"const": "foo"},
     "multipleValues": {"enum": ["foo", "bar"]},
diff --git a/spec/fixtures/expected-schema-from-draft-04-to-2020.json b/spec/fixtures/expected-schema-from-draft-04-to-2020.json
index ccb1222..3daac4a 100644
--- a/spec/fixtures/expected-schema-from-draft-04-to-2020.json
+++ b/spec/fixtures/expected-schema-from-draft-04-to-2020.json
@@ -10,6 +10,29 @@
       "$id": "another-schema",
       "$anchor": "num",
       "type": "string"
+    },
+    "exclusiveMaximum": {
+      "$ref": "http://json-schema.org/draft-07/schema#/properties/exclusiveMaximum"
+    },
+    "maxLength": {
+      "$ref": "http://json-schema.org/draft-07/schema#/definitions/nonNegativeInteger"
+    },
+    "parametersList": {
+      "type": "array",
+      "description": "The parameters needed to send a valid API call.",
+      "items": [
+        {
+          "oneOf": [
+            {
+              "$ref": "#/definitions/parameter"
+            },
+            {
+              "$ref": "#/definitions/jsonReference"
+            }
+          ]
+        }
+      ],
+      "uniqueItems": true
     }
   },
   "properties": {
@@ -21,6 +44,12 @@
       "minimum": 1,
       "maximum": 3
     },
+    "exclusiveMaximum": {
+      "$ref": "#/definitions/exclusiveMaximum"
+    },
+    "maxLength": {
+      "$ref": "#/definitions/maxLength"
+    },
     "singleValue": {"const": "foo"},
     "singleValueConstant": {"const": "foo"},
     "multipleValues": {"enum": ["foo", "bar"]},
diff --git a/spec/fixtures/schema-draft-04.json b/spec/fixtures/schema-draft-04.json
index 896d480..a5d5def 100644
--- a/spec/fixtures/schema-draft-04.json
+++ b/spec/fixtures/schema-draft-04.json
@@ -9,6 +9,28 @@
     "num": {
       "id": "another-schema#num",
       "type": "string"
+    },
+    "exclusiveMaximum": {
+      "$ref": "http://json-schema.org/draft-04/schema#/properties/exclusiveMaximum"
+    },
+    "maxLength": {
+      "$ref": "http://json-schema.org/draft-04/schema#/definitions/positiveInteger"
+    },
+    "parametersList": {
+      "type": "array",
+      "description": "The parameters needed to send a valid API call.",
+      "additionalItems": false,
+      "items": {
+        "oneOf": [
+          {
+            "$ref": "#/definitions/parameter"
+          },
+          {
+            "$ref": "#/definitions/jsonReference"
+          }
+        ]
+      },
+      "uniqueItems": true
     }
   },
   "properties": {
@@ -24,6 +46,12 @@
       "maximum": 3,
       "exclusiveMaximum": false
     },
+    "exclusiveMaximum": {
+      "$ref": "#/definitions/exclusiveMaximum"
+    },
+    "maxLength": {
+      "$ref": "#/definitions/maxLength"
+    },
     "singleValue": {"enum": ["foo"]},
     "singleValueConstant": {"constant": "foo"},
     "multipleValues": {"enum": ["foo", "bar"]},
diff --git a/spec/migrate.spec.ts b/spec/migrate.spec.ts
index c6fed0a..7fc5780 100644
--- a/spec/migrate.spec.ts
+++ b/spec/migrate.spec.ts
@@ -34,7 +34,7 @@ describe("migrate to draft-07 schema", () => {
 
   describe("invalid schemas", () => {
     it("should throw if id is not a string", () => {
-      assert.throws(() => draft7({id: 1}))
+      assert.throws(() => draft7({id: 1 as unknown as string}))
     })
 
     it("should throw if id has many #s", () => {
diff --git a/src/index.ts b/src/index.ts
index 9bd444d..c496dec 100644
--- a/src/index.ts
+++ b/src/index.ts
@@ -107,6 +107,22 @@ export function getAjv(): Ajv {
           case "exclusiveMaximum":
             migrateExclusive(dataSchema, key, "maximum")
             break
+          case "$ref": {
+            const val = dsCopy[key]
+            switch (val) {
+              case "http://json-schema.org/draft-04/schema#/properties/exclusiveMaximum":
+                dataSchema[key] =
+                  "http://json-schema.org/draft-07/schema#/properties/exclusiveMaximum"
+                break
+              case "http://json-schema.org/draft-04/schema#/definitions/positiveInteger":
+                dataSchema[key] =
+                  "http://json-schema.org/draft-07/schema#/definitions/nonNegativeInteger"
+                break
+              default:
+                dataSchema[key] = val
+            }
+            break
+          }
           case "exclusiveMinimum":
             migrateExclusive(dataSchema, key, "minimum")
             break
@@ -129,16 +145,19 @@ export function getAjv(): Ajv {
             }
             break
           }
-          case "items":
+          case "items": {
             if (version === "draft2020" && Array.isArray(dsCopy.items)) {
               dataSchema.prefixItems = dsCopy.items
               if (dsCopy.additionalItems !== undefined) {
                 dataSchema.items = dsCopy.additionalItems
               }
+            } else if (!Array.isArray(dsCopy.items) && dsCopy.items.oneOf) {
+              dataSchema.items = [dsCopy.items]
             } else {
               dataSchema.items = dsCopy.items
             }
             break
+          }
           case "additionalItems":
             if (version !== "draft2020") {
               dataSchema.additionalItems = dsCopy.additionalItems