Don't know if that's possible. The R3's engine is based on the R25, but has a bore of 68mm to the R25's 60mm. Since the case is the same size there probably isn't any more room to go with a bigger bore.
Someone could make a kit with shorter connecting rods, maybe, and get more cc's with a shorter stroke.....That might change engine dynamics in a negative way, though.
42hp out of a 320cc twin is pretty impressive ,doubt you wring more than another 8 to 10 out of it
I am currently looking into R & D ing a turbo kit for the R3.
In the past a few custom builders have had success successfully fitting a turbo to a ninja 250 and cbr 250.
They made about 60hp.
A parallel twin engine design is very reliable built like a tank and go go 100k plus miles no problem so turboing even if shortening lifespan to 60k miles is fine with me.
I use to ride a kawasaki ninja years ago in 2004 and always wanted to turbo charge it. Still no big name manufacturers are making turbo kits for the 300cc class of sport bikes but it is possibly to piece together a kit and do a custom install yourself.
Two things I want to get right are,... larger injectors for the R3 Can anyone recommend any? I can frankenstyein some off another bike if need be such as the pcx 150 injector. And will need a new ECU with auto-tune and programmed to flow more fuel at higher rpm when boost kicks in. Everything else is a cakewalk just bolt on stuff and a custom welded header.
Even the honda grom (which is what I ride now) has a turbo kit out for it.
This turbo for the grom is Tiny and also used on yamaha zuma 125cc scooters. Its good for a 6-7 Hp increase on the smaller engines So this could be adapted to a twin turbo set up as well LoL. Two of these hanging off each exhaust outlet for a total hp improvement of 14hp on the R3. Or could just go with the smart car garett gt26 turbo as used on the other ninja 250's.
People will always say just buy a bigger bike but then it takers some of the fun out of having a smaller bike to begin with. Its either turbo charge a r3 to 60hp or buy an old Honda NSR 250cc two stroke then throw on a tyga 300cc BBK to get to 65-70Hp.
Always wanted a small 60-65hp bike and sooner or later will make that happen.