Everyone I know has a problem with doubling (trebling etc etc). I grew up on clarinet and have always found the soprano a completely natural follow-on - same-ish size, straight, same pitch. Alto is the horn I've been on most in jazz combos and then I got a Rock gig and needed a tenor. Like Colin, I haven't found this as natural as the others. It certainly isn't a bigger alto.The tenor isn't a bigger alto. It's similar but completely different. It may take a lifetime to get the tone you want from a tenor. Bear in mind though that they don't sound the same behind the mouthpiece as they do in front. Practice cures most problems. You have to earn your tone. You cannot buy it.
My own experience was...Clarinet no problem Add alto no problem. Add Baritone no problem. Add tenor oh dear squawk, squeak, poor intonation and poor tone. Eventually improving. Add soprano... shouldn't have bothered...stupid thing...house is full of dogs and bats.
Many gravitate from alto to tenor, but few continue to specialise on both. Who has heard Sanborn on tenor, or Brecker on alto (to name but two)? Brandon Fields has played more tenor recently, like Andy Snitzer, but he also sounds great on baritone, and soprano. I think he comes from the old school of being a woodwind player though, like Tom Scott (check his Joni Mitchell stuff in the early 70's) and plays a lot for film covering most of the axes, like Sal Lozano also.
I can leave all axes for a while and get them back pretty fast - but not tenor. The only way to be competent on more than one horn is to alternate them in practice. It takes a certain approach though, to be happy to put a horn down when you are not happy with it and go at another.