A technique we've used to deal with this situation: in the overloaded backend (that has to reject some percentage of incoming requests), group the incoming requests by the parent request (the one with the 1:15 fan out) and reject according to the parent request. One way to put it, simply (though somewhat inaccurately), would be: reject 100% of traffic from 20% of users, rather than 20% of traffic across all users (causing essentially full failure for all users).
We typically implemented this by propagating an ID of the parent request down to the backend. I'm simplifying a lot in this description (e.g. have to deal with the parent requests landing on different backend tasks; also rotate the IDs gradually to introduce some fairness).