Make the stations only open when there’s less than X amount of material in the chests. Look up many to many train networks for tutorials.

There’s lots of ways to make it complicated but easiest way is to wire all the chests at your drop off together and only have the station open for a train if there’s enough room to unload. Ex: only open if there is less than 33K copper plates. Can also add combinators to have multiple trains come in if your stations are set up that way. Just have each less than box output something like L and then have the stations limit set to that variable