There is no way one can improve the UX without changing the interface. UX is not something which you can design, it is always the UI which you design where you see that the interface delivers best UX. Any changes in the experience will have the direct impact on the UI and the interactions.
Yes, when it comes to not changing the UI means maybe we can consider it as the visual guidelines which are defined for the whole product. Within that one can improve the UX.
UX is an experience which you define using the interface so it is part of it. The fundamental thing to remember is there is nothing like I can give good UX Design, you always can give a good UI design only which in turn gives a good experience. So, UX is not designed.