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If you're worried about starting rsync sessions over and over (slow) then make a temp copy, or tar archive, locally and rsync once afterwards,

for x in `find ~ -name files*`; do tar -uf work.tar...

I'm sure rsync doesn't have a built in way to do that.

You would have to write a command loop like:

for x in `find ~ -name files*`; do rsync $x server:/backup/; done

see man find for...