Inserting a note changes previous notes?

What you want is the musical equivalent of a word processor where if you put the cursor in the middle of “supercalifragilisticexpalidocious” and type something in insert mode, what you type appears after the end of the word.

Except most people would want the letter to appear where the cursor was, if they put the cursor after the “exp” and inserted the letter i to fix the typo.