I was TUPE transferred five times.

As stated above you automatically transfer on the same terms and conditions without the need to sign a new contract.

Your new employer may well offer you a new contract to eradicate the TUPE protection.

I think the only catch is that you are not entitled to pay increases that may relate to your old job.

Pensions are also complicated.

Your employer must consult with you and your new employer will want to talk to you.