It depends what you mean by a separate domain. The sharing/collaboration works well when it is a primary and secondary domain. We have students (primary) and staff (secondary), controlled via the one admin console. There are some limitations - https://support.google.com/a/answer/182081.
However if it is a completely separate domain, I do not believe there is much that can be done. There is whitelisting available for Drive which may be of some assistance - https://support.google.com/a/answer/6160020.
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