SS preamp to replace BAT VK3i w/ht bypass

If you like the BAT house sound, go BAT again. Another way to go is the Bel Canto Pre-1. I doesn't seem to have much sound of it's own. It is more transparent and neutral than the 3i. Of course you'll lose the bloom that the 3i is known for. It is also less muted and has better pace. It really allows me to enjoy the sound of my BAT D5 player, without robbing it's character by imposing more tube or transister artifacts.

The Jeff Rowland Synergy IIi is a great preamp that is fully balanced and has a home theater by-pass.

I am using a SS Muse 3 Signature, which I find to be outstanding. It is fully balanced, with 2 XLR and 3 RCA inputs, and one set each of XLR and RCA outputs. It also has an HT pass through, which is activated with a single press of one button on the remote. Input gain can be individually adjusted to normalize output between different sources, and it also has a polarity inversion switch. Muse considers this preamp a "statement product," and (in my system anyway) I have found it to be very musical and dynamic, with a rich midrange, beautiful grainless high frequencies and deep powerful bass. It stays on all the time in a standby mode, so it is ready when you are. I use it with a BAT VK500 and there is good synergy. I believe the new price is about $2300, and I doubt you will find one used. Although YMMV, I would strongly recommend an audition based on my positive experience with this unit, and your stated criteria. The BAT VK 40 is also said to be very good.

Second the recommendation of the Rowland Synergy IIi.