Need help with upgrade path

I'm using a BAT VK-300x integrated with vr4jr speakers and need your advice on an upgrade path to balanced separates. I can try different amps while still using the pre-amp section of the integrated but I'm not sure it is up to the job. As it is now I can't audition a preamp so I plan on upgrading this later.

I'm looking for an amp with better bass control and more oomph while still being nimble and detailed on a budget of 3k to 5k. Some of the amps I'm considering: BAT VK-250 or VK-500, Parasound JC-1's, Ayre V-5xe or Spectron M III.

I appreciate your helpful insights in this quest.