Everything is possible, but depending if you're full of money or if you've got luthier skills..
Mustang tailpiece sucks, if you don't use the vibrato put a gibson tailpiece and a TOM instead..
So go back to your mods 😁
To do it you have to remove the old tremolo unit, sand the internal cavity of the tremolo and put a piece of wood inside and that's really not easy..
sand to have a beautiful flat surface on the both sides, routing for the mustang tremolo unit, drill the hole at the good place to keep the good scale..
That's not finish, you have to keep a good sting line from the neck to the bridge, an error less 1 milimeter may srew up.. after that you certainely need to shim your neck..
It's very hard to explain very well 'cause I have bad english, but it's a big big job, very interesting !