I have the Studios as well, and really, really like them.
However, I use a Mark Levinson No. 23 amp (SS with 200W/ch.) The additional power really helps open up the sound, especially in the bass.
It seems to me that you are going to have to make a decision, to either switch out the Studios (which are a bit power hungry), or switch to a more powerful amp (and since you currently use an integrated amp, that might mean switching to seperate preamp and amp).
My advice would be to ask your dealer to lend you a more powerful amp (if you have a preout on your BAT, you won't need to borrow a preamp). Then make the decision on whether that is the sound you are going for. (It is typically easier to get lent amps and/or preamps from your dealer, than speakers. If you are going to buy new, the dealer should be willing to help you out.)
As far Sgr's recommendation to use Adcom, I am not sure about that, as I think the quality of Adcom is below that of both the BAT and the Studios. (However, I have not seriously heard Adcom for quite a few years. If Sgr says they have improved in quality in the last 5 or 10 years, then this might be a good avenue to explore, as they are less expensive. I would recommend any of the better and more powerful SS units (ie. Levinson, Krell, Rowland, etc..)
My two cents worth, anyway. Good Luck!