You can precomp the 10 footage layers together and use the mask as a track matte in the main comp.
If that's not possible you can precomp the mask layer. Duplicate it 10 times and set the track matte for each footage layer. The reason for precomping the mask layer is so that if you need to make changes to the one mask it will ripple through to all of the duplicates.
You can also use expressions to link masks on duplicated mask layers instead of precomping, so whatever works best for you.
You can also precomp the mask layer with the footage and set the blending mode to stencil alpha or silhouette alpha. But make sure you don't collapse transformations or it will cut out the background as well (defeating the purpose of precomping the layers).
I'm sure there are other options, but those are the ones I would try first.
If you want exactly the same mask on all the layers then I'd pre-comp the mask layer, apply a Set Matte effect to the layers you want to mask and point it to the mask pre-comp. The pre-comp does not need to be visible.