People are going to tell you to do searches because this exact question was asked about 50 times. haha But I never replied to any of um so I'll answer you.
1st of all, if you want to trun your Corolla into a speed monster to compete with STis, Evos, Supras and what not, you'll need a really large, large amount of cash.
2nd the 2jz is an inline 6 cylinder engine and would not fit in the Corolla engine bay transverse being a front wheel drive car. If you had the cash to do it, you'd need to convert the car to rear wheel drive which is not too good because it wouldn't be a balanced car or so I've heard.
Even the possible engine swaps are expensive because parts will have to be custom made, like engine mounts.
But possible swaps are the Celica GT-S, Corolla XRS 2zz-ge
Or the JDM 4a-ge super charged version available.
or the 3sgte turbo charged version available.
Or you could just turbo your 1zz-fe.
Each of these options would have you out running Supras but they will be able to hold their own.
-Someone please correct me if I was wrong at any point.