send Fill & Sign form for somebody else to forward onto multiple different recipients

I have a blank GDPR release form (for consent to be filmed).  This will need to be filled in and signed by the parents of various children at a school - a new copy of the same form for each child.

For both GDPR and child protection reasons, the school will have to send the form out to the parents of any children we need permission from.

Is there a way that I can send a blank version of the form to the school, having marked the sections that need to be filled/signed, for them to then forward it to any parents we need to complete it, as and when we ask them to? (i.e. can they forward it to an unlimited number of people – not necessarily all at once – with each person signing a separate copy of the form?)

If this is possible, how do I do it?