tmux has the "move-window" command with which you can move a window to a specified empty index like so:
move-window -t 3
However, if index 3 is already taken you will not be able to move your current window to position 3.
I'm looking for an option that will allow me to move (insert) my window at position 3 even if it is already taken and then increase the window numbers for the other subsequent windows (for example the one that was originally at 3 will now be 4, the following will be 5 etc.)