Stratified Random Sampling by ID in QGIS?

Question

I've been playing around with the Random Points tool in QGIS to realize stratified random sampling, but I'm running into a problem where I want my strata to be based on a polygon ID, not each individual polygon. In other words: I may have multiple non-contiguous polygons that all represent a single strata, where I want a TOTAL of (e.g.) 10 points randomly distributed among the disconnected polygons, not 10 per polygon. Is there any way to do this? Would a multi-part polygon work, for this?

Answer 1

Using a multi-part polygon does work. Below, a multi-part (blue) and single polygon:

Using the random points tool and 20 points per polygon, 20 points are distributed amongst all three blue parts of the first polygon: