Dire Bare
Legend
What if they had wanted to play another android like Data? A Klingon isn't that hard to justify even if someone wanted to keep Worf the only Klingon in Starfleet - they'd just have to be part of the officer exchange program that we saw in "A Matter of Honor" from season 2. Then, the'd still be part of the Klingon Empire as well as available on a Starfleet vessel - lots of plot hook connections both ways.
But Data really is supposed to be unique. You could come up with yet another Soong android, but that really would cheapen the chachet of being an android if you're just going to retcon more as you need them.
Of course, the most obvious alternative... if you want to be an android like Data - play Data.
Within Star Trek lore we have plenty of androids other than Data. Within the Next Gen series, we had B4, Lore, Soong's android wife, and perhaps others I'm not remembering. Adding one more for the player character hardly seems a problem. I seem to remember android characters from the original series also. In the latest show, "Picard", more androids is a major developing plot!
And even if Star Trek canon had stuck with "the only sentient android in existence is Data, there are no others" . . . . I would totally allow an android in my Star Trek tabletop game. Player fun trumps sticking to the canon of a TV show, especially when the TV show itself doesn't really worry that much about it.