diff --git a/e2e/builder/global_test.go b/e2e/builder/global_test.go
index 1e2650becc..0e0cd5db10 100644
--- a/e2e/builder/global_test.go
+++ b/e2e/builder/global_test.go
@@ -25,8 +25,10 @@ import (
 	"os"
 	"testing"
 
+	camelv1 "github.com/apache/camel-k/pkg/apis/camel/v1"
 	. "github.com/onsi/gomega"
 	"github.com/stretchr/testify/assert"
+	metav1 "k8s.io/apimachinery/pkg/apis/meta/v1"
 
 	v1 "k8s.io/api/core/v1"
 
@@ -49,14 +51,17 @@ func TestRunGlobalInstall(t *testing.T) {
 	WithNewTestNamespace(t, func(ns string) {
 		Expect(Kamel("install", "-n", ns, "--global").Execute()).To(Succeed())
 
-		// NS2: namespace without operator
+		// NS2: namespace without operator but with platform
 		WithNewTestNamespace(t, func(ns2 string) {
+			// Creating platform
 			Expect(Kamel("install", "-n", ns2, "--skip-operator-setup", "--olm=false").Execute()).To(Succeed())
 
 			Expect(Kamel("run", "-n", ns2, "files/Java.java").Execute()).To(Succeed())
 			Eventually(IntegrationPodPhase(ns2, "java"), TestTimeoutMedium).Should(Equal(v1.PodRunning))
 			Eventually(IntegrationLogs(ns2, "java"), TestTimeoutShort).Should(ContainSubstring("Magicstring!"))
 			Expect(Kamel("delete", "--all", "-n", ns2).Execute()).To(Succeed())
+			Expect(Kits(ns2)()).Should(HaveLen(1))
+			Expect(Kits(ns)()).Should(HaveLen(0))
 
 			Expect(ConfigMap(ns2, platform.OperatorLockName)()).To(BeNil(), "No locking configmap expected")
 		})
@@ -75,6 +80,56 @@ func TestRunGlobalInstall(t *testing.T) {
 			)
 		})
 
+		// NS4: namespace without operator or platform
+		WithNewTestNamespace(t, func(ns4 string) {
+			Expect(Kamel("run", "-n", ns4, "files/Java.java").Execute()).To(Succeed())
+			Eventually(IntegrationPodPhase(ns4, "java"), TestTimeoutMedium).Should(Equal(v1.PodRunning))
+			Eventually(IntegrationLogs(ns4, "java"), TestTimeoutShort).Should(ContainSubstring("Magicstring!"))
+			Expect(Kamel("delete", "--all", "-n", ns4).Execute()).To(Succeed())
+			Expect(Kits(ns4)()).Should(HaveLen(0))
+			Expect(Kits(ns)()).Should(HaveLen(1)) // Kit built globally
+
+			Expect(ConfigMap(ns4, platform.OperatorLockName)()).To(BeNil(), "No locking configmap expected")
+		})
+
+		// NS5: second namespace without operator or platform, using an external kit
+		WithNewTestNamespace(t, func(ns5 string) {
+			Expect(Kamel("run", "-n", ns5, "files/Java.java").Execute()).To(Succeed())
+			Eventually(IntegrationPodPhase(ns5, "java"), TestTimeoutMedium).Should(Equal(v1.PodRunning))
+			Eventually(IntegrationLogs(ns5, "java"), TestTimeoutShort).Should(ContainSubstring("Magicstring!"))
+			Expect(Kamel("delete", "--all", "-n", ns5).Execute()).To(Succeed())
+			Expect(Kits(ns5)()).Should(HaveLen(0))
+			globalKits := Kits(ns)()
+			Expect(globalKits).Should(HaveLen(1)) // Reusing the same global kit
+			if len(globalKits) == 1 {
+				kit := globalKits[0]
+				// external kit mirroring the global one
+				externalKit := camelv1.IntegrationKit{
+					ObjectMeta: metav1.ObjectMeta{
+						Namespace: ns5,
+						Name:      "external",
+						Labels: map[string]string{
+							"camel.apache.org/kit.type": camelv1.IntegrationKitTypeExternal,
+						},
+					},
+					Spec: camelv1.IntegrationKitSpec{
+						Image: kit.Status.Image,
+					},
+				}
+				Expect(TestClient().Create(TestContext, &externalKit)).Should(BeNil())
+
+				Expect(Kamel("run", "-n", ns5, "files/Java.java", "--kit", "external").Execute()).To(Succeed())
+				Eventually(IntegrationPodPhase(ns5, "java"), TestTimeoutMedium).Should(Equal(v1.PodRunning))
+				Eventually(IntegrationLogs(ns5, "java"), TestTimeoutShort).Should(ContainSubstring("Magicstring!"))
+				Expect(IntegrationKit(ns5, "java")).Should(Equal("external"))
+				Expect(Kamel("delete", "--all", "-n", ns5).Execute()).To(Succeed())
+				Expect(Kits(ns5)()).Should(HaveLen(1)) // the external one
+				Expect(Kits(ns)()).Should(HaveLen(1))  // the global one
+			}
+
+			Expect(ConfigMap(ns5, platform.OperatorLockName)()).To(BeNil(), "No locking configmap expected")
+		})
+
 		Expect(Kamel("uninstall", "-n", ns, "--skip-crd", "--skip-cluster-roles").Execute()).To(Succeed())
 	})
 }