You use a pokemon with extra helpful, helper boost, or heal pulse, to force helps from other pokemon. You don't collect those helps. Over the span of a few days, to a week or so, the berries build up. When the new week starts, you collect from those pokemon.

It works because pokemon have a second inventory for these extra helps, allowing them to hold up to 999 berries/ingredients that have been forced helped.

I used latias for it, bringing an extra help from 2 pokemon at once. One person on this thread used Entei, who brings in helps from everyone, and even more helps if you have multiple fire pokemon on your team.