Matching a preamp with a different brand

You really can't trust specs to give you the whole picture. Not everyone measures them the same way. The only way you can really know for sure, is to try the preamp with your components. If you can't do an in home demo, most dealers will have no problem with you bringing your components into the store. If you list your system and what you expect from the upgrade, you'll get better answers.

The input impedance of the amp should be ten times or more
than the output impedance of the preamp. The output voltage of
the preamp should be the same or more than the input sensitivity
of the amp.

^^ This, plus if possible find out what the output impedance is at 20Hz; is it still fitting into that 10:1 ratio? If so that is very good as bass will not be compromised.

Thanks Atmasphere, I just read about a BAT amp matching up with other preamps brands challenging.

I've seen BAT amps used with many different brands of preamps. But why not consider a BAT preamp? They make some nice ones in both tube and SS.

Assuming an active pre-amp, mostly just making sure both share a common physical connection standard and following the 10:1 impedance rule from there. The fun all starts from there. No two combos will sound exactly alike, but at least you have done what you can to help assure they get along together as best possible.