just in the interest of conversation and imagination.

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i also had a 4wd sw20 idea a while back.

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there are 2 ways of doing it.

1,
the horid way.

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put a scooby lump in the front and bodge the 4wd system to fit.

but you ruin the balance of the car and it'll basicly be a bad version of the celica gt4.

2,
cut the diff off the gearbox.

graft on a transfer box with diff so that the prop could go where the exhaust is.

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move the exhuast to find another way out of the back.

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the fuel tank needs moving or reshaping.

prolly making it a lot smaller.

then you need front hubs that can take drive.

maybe celica ones? not looked into the 2 designs.

front props and a diff.

not too hard to sort out.

would need to chop up frunk floor to fit this and then weld in some extra supports to make up for the missing bits and extra weight.

the battery would need to be moved too.

the expensive bit is making the transfer box fit the gearbox.

once you have this sorted the rest is quite simple.

but i dont think the mr2 has bad turn in at all.

i think its got quite a lot of front end grip.

what tyres are you using? have you had a proper 4 wheel alignment done? have you uprated the suspension in anyway? strut braces?