You might want to look at animator overrides:
https://docs.unity3d.com/Manual/AnimatorOverrideController.html
I'm not exactly sure how well-suited the demo animator is for overrides, there was a topic about this recently:
https://opsive.com/forum/index.php?...e-controller-interrupt-current-movement.6342/
To be honest, in the case of having different animations for a single character/object based on items, the expected thing would be to still use a single animator controller with more substates. But I know that animator controllers can get quite complex and hard to manage. Unfortunately I think this is partially just a limitation of Unity's animator setup - perhaps there are other third-party assets/tools out there that might help with this.