No NO NO NO.
A type rating is something which needs to be placed on your license after a course with a TRTO. And costs a **** load of money.
Differences training between different SEP variations is completly up to the person who owns the plane. Taking aside any difference training you require to operate wobberly props retractable gear, complex types etc
I and most other instructors ex or current have jumped into aircraft which we have never flown before or have been "checked" out on and flown them. You read the book and then pick out the things that will kill you and fly it.
If you get permission from the owner you can fly it. ITs down to you as PIC to self limit your flying to what you are capable of. You can have 1 landing or 3 or 25. Its up to you to say if you are capable of flying it or not.
3 landings doesn't teach you how to operate a machine.
Sorry to sound harsh but its all part and parcel of being the PIC.
MJ