Of course, if the George Bush the Elder won in ‘92, he would have done just that.
IIRC, the VP can only take over for just a little UNDER 2 years and then he/she could be elected to President twice. The key is in the Constitution, two terms with a maximum 10 years. The only case I know of where that applied recently was with LBJ after JFKs demise. He could have run twice but didn’t run the second time because of Viet Nam.