Can anyone recommend the simplest and cheapest way to grow into a second plane while still keeping the first one flyable and not having to buy another radio? Is this possible?

I'd suggest the H9 Ultra Stik 40, TT-46 Pro and Hitec's flight pak.
This gives you a good transition from your trainer.

The standard practice is to have one transmitter and any number of models, each with its own receiver and servos installed. You don't need more than one transmitter, but every model needs its own receiver, battery, switch and servo set--known in the hobby trade as a "flight pack" (which may or may not include the other necessities--receiver crystal for the same frequency as your transmitter, and switch harness for recharging the receiver battery and turning on/off). Flight packs go for maybe $120.

I suppose for utmost economy you could swap one receiver between two models, but you need to be sure receiver and battery are securely mounted (with foam rubber protection against airframe vibration) so they don't flop around when you do loops and turns. Flopping around is bad, makes things crash.

I thought that GP made the Ultra Sport? Unless you were talking about the Ultra Stik which makes more sense and probably a better second plane. My second plane was an Easy Sport by GP that I built. Can't go wrong with it. Easy to build and you can get valuable learning experience or get it in ARF form. Also, try the Slowpoke Sport 40. Not a blazer in the sky, but it is as stable as can be on approach and flies very easy.

My second was an EasySport also. Had a TT 46 on it.
I loved that plane... Loved it right into the ground...

Good catch -- I did mean the Ultra Stik -- too many Ultra's out there.

See Jazzy, that gave you two more of those foam tires your after.

dq2: I had the same problem a few( lots of) years ago. But now with 20+ planes I have 8 Rx's, 2 Tx's and must be a million of them little servos. Once the servos are in and trimmed out, it's
much easier to pull the Rx and switch planes. Just a word of warn-
ing that if you stay in the hobby, those planes tend to propagate
in dark places. Most suppliers offer the flight paks with a Rx. , 4 or 5 servos and a switch- that will be cheaper than buying one at
a time.

As far as a second plane, i have to agree with the Ultra Stik reccomendation. My 2nd plane was a very old used .40 Stik (not sure what brand, not an ARF though). It was just as easy to fly as my trainer, maybe even easier, and a lot more fun. I didn't stick with it too long though cuz i really wanted a scale plane. The stick was an easy handler and landed very gently.

My main plane now is the GP Extra 300S .40. Some people could probably get away with it as a second plane, but i wouldn't reccomend it. Surprisingly gentle for a real aerobat though.