as was said, don’t worry about ‘too much of a good thing”.
Tube amps can be quite versatile in their voice, depending on which tubes are in use, or which tubes are available as ‘drop in’ replacements.
a BAT tube pre plus a BAT SS amp has been a great combo for a long time in BAT land.
one thing of note is running BAT pre and amp balanced is a very good idea. no question about it. extremely quiet back drop which aids gaining a more vivid presentation and imagery.
another built in item is the BAT ‘house’ sound. you do get the synergy which comes with keeping the same brand in the signal path.
adding another non BAT line stage but which runs truly balanced will act similarly of course.
that said, adding a line stage which is far higher on the food chain which runs SE only will still yield great results. or such is my own EXP.
remember, with many though not all line stage tube amps, you can either dial up the ‘tubeyness’ or dial it down via a bit of tube rolling.
with SS line stage amps you’re stuck with whatever ;’voice’ it offers, which BTW is not a bad thing either.
good luck with your decision.