Cornwall IV – new amp vs crossover upgrade

I recently bought Cornwall IVs and basically I´m very happy with them – they just sound very pleasant. And I haven´t even upgraded to another amp yet which seems to be the next logical step. When I was in the store I tested them with a class AB and a hybrid amp and I could already tell that the hybrid made them sing. Currently I´m using an old, small Rotel amp and they do sound great with it but I know there´s plenty of room for improvement.

Having read a few things here and there, I´m wondering which has the bigger impact: a new amp or a new set of crossovers. Sure, it´s all individual but with people raving about non-Klipsch-crossovers and other improvement (for example damping the horns as suggested by the Boston Audiophile), I´m not exactly sure what should be next. Would a nice tube amp make a crossover upgrade unneccessary? It´s hard to tell from what I´ve read.

As much as I like them, I feel right now they are lacking a bit of overall warmth. On the other hand the highs are a bit too pronounced and detailed for me which led me to turn down the highs on the amp a bit. There are some recordings that just match the current setup and listening to them puts a big smile on my face. And I just feel that this can be extended to more albums.

Thanks in advance for help and suggestions!