This does not dupe Why can’t I push from a shallow clone?, because I am asking specifically about partial clones. No use of the --depth filter here.

Starting with a “blobless” clone:

git clone --filter=blob:none https://example.com/a-repo.git

I have added a new remote (it exists, and is empty) called “lite”

git remote add lite https://example.com/b-repo.git

A git push -u lite HEAD references origin and pushes all the blobs. At least, that’s what I think it was doing because it printed out the origin url and tried to push a lot of objects.

Can I only push the trees and currently available blobs to “lite”?