I am curious about this question as the 2.3 DISI is a fantastic engine for tuning, not to mention it sounds fantastic. Would it be possible to buy a wrecked Mazda 3 MPS and get the engine and gearbox to fit?

Would it be possible to buy a wrecked Mazda 3 MPS
Probably quite easy...

and get the engine and gearbox to fit
I doubt it, although I don't know the answer, they are built on very different platforms.
The MPS is similar to a Ford Focus underneath.
The BA was designed over a decade earlier, and is based on the BG 323.

But nothing's impossible with enough time and money.
If I was thinking of what you're suggesting then I'd go for a V6 BA.

Hmm. Even if the engine and box did fit, obviously you'd also have to upgrade the running gear all round, to handle it. I'm assuming the candidate BA would be your 1.8? It has better front brakes than the 1.5 (well, the 1.8 actually has brakes, so let's leave it at that!) but if you tried to stop a 2.3 250hp turboed engine with brakes and running gear intended for a 1.8 114hp with drums on the rear, I don't fancy the outcome. Let's not even imagine trying to do this to a GXi *shudders*

And then there's the wiring loom.

I don't like squelching happy car dreams, but I agree with JB. If you want a major engine upgrade for your BA I think you're better off just finding a V6, and if a 2.0 KF isn't enough then find a 2.5 KL to drop in it; or if power is more important than being in a BA, just buy a non-wrecked 3 MPS. Otherwise your BA is likely to be off the road for some time having a LOT of surgery, and if it didn't work after all that, the extent of modifications might make the car unusable even if you put the 1.8 back in.

S