You could do something similar with sequences and triggering via MIDI in the performer panel.
Duplicate your stage and set the merge mode to 'add' to get a 2nd layer since you want to overlay an effect on top of your stage. Then go in the sequences menu and create a group for the duplicate stage.
You can then create a sequence with 2 steps. Step 1 is the effect you want to overlay with the duration you want (for example 1 second) and step 2 is a blank media with a very long duration (like 9999 seconds). This 2nd step is a kind of workaround to get a single run since in the performer, there's no 'single run' play mode. Adding this play mode might actually be a good idea in a future version.
This way, in the performer panel, each time you trigger your sequence, it will play your effect once.