Every engineer's week is already on the screen: hours booked, hours available, what is due when. You enter the support request as roles and hours - say, 12 developer hours by Friday - and see each person's this week and next before and after, with the other work that is due in the same weeks.
The options are laid out side by side: take it as proposed, one week longer, another person with the same role, or hold. Each shows its own numbers. You choose; the decision and the numbers it was made on are kept with the request.
Standing work - a support rota, on-call - is held as hours per week, so an issue that lands inside the rota does not count twice.