Alternative gearbox?

[Fairway1]

Hi guys, I have a 2005 Corolla 1.6 petrol with the 5 speed manual gearbox. The engine has E3Z - Y52R markings on the side.

This maybe a stupid question, but is there a six speed gearbox off another model that would fit my car? The 5 speed feels a bit low geared for regular motorway use and I'm soon going to be replacing the clutch, so I was just wondering before I start this work if anyone had swapped for a 6 speed because I could do it at the same time and maybe bring the revs down a little when cruising along motorways.

Many thanks

[flash22]

That will be the 3ZZ 1.6