Does any terminal multiplexer (screen, tmux, zellij) support job suspension (Ctrl-Z) in Bash?

As far as I've seen, pressing Ctrl-Z on any terminal multiplexer, or trying to start them in the background, does nothing or crashes. I know that, in a sense, terminal multiplexers are a "replacement" for job control, and usually, they have their own mechanisms for suspending and resuming. Still, I was wondering if I could integrate them in some way into a workflow based on the shell's job control. **Answer:** - Screen suspends with "C-a z" - Tmux suspends with "C-b C-z" - Zellij suspends with "C-o d", but unlike the previous ones, it doesn't place the process on the shell's job control.