Each trust is a separate entity, the fact that the trustee is the same "person" for all of them does not change anything.
That being said, if it is not against policy or legal counsel's advice, you could probably come up with an all-encompassing document.
One potential issue with this route could be privacy - if you are ever in a situation where you need to present signature cards to someone for one of the trusts (think in a face of a law suit or trustee mismanagement challenge), you would potentially be disclosing all the information for other trusts that is included on this signature card.
Opinions are my own.
"I was gratified to be able to answer promptly. I said I don't know." - Mark Twain