Possible to render a mesh above all other meshes but with exceptions?

Hello, Sure is.
In fact there are a number of methods for this.
Speaking about one single mesh and just a shortlist of exceptions and assuming these are all and will remain in the scene, I would look at layerMask or renderingGroupId (or a combination of both).
In-Depth layerMask

Else, if you set-up a quick PG to test the feature, I’m sure someone in this forum (including me) will help you find the best way for your needs.

Edit: May be have a look at this recent post that is probably quite similar to your needs (except you would push an array to use one of the layerMasks for your exception list)