You can use a setup like this, restricting the number of items going a certain direction by pipe bandwidth.
The principle is that each brass pipe can only pass one item per second, but the hopper will output items into the center (high-capacity) pipe at least 4 per second, so the items will have to take different paths. The center hopper is set to output an exact stacksize of 1 item, so that each stack being pushed through is only one item. The side hopper is if you don’t have a large number of items, and is set to emit a multiple of 4 items. This is optional if you have a large supply of items to distribute, and is meant to prevent items being sent out if there is less than 4 and balancing isn’t possible. Either way, it seems like this setup can come out slightly unbalanced (in my testing, one extra item was in one chest, and missing from another chest), which I figure is some interaction between the timing of the hopper output and when the pipe sends the items out. I used this in a previous world to balance hydroxide recirculation in a multi-autoclave alumina setup.
Note that this does not work if the brass pipe branches are longer than 1 pipe. This is because the pathfinding algorithm for item pipes marks searched pipes as marked even if they aren’t on the ultimately travelled path, because they are nonphysical and unintuitive like that. If the path is only one pipe long, it looks like items are immediately put into acceptors connected to a visited pipe, so only one pipe will get bandwidth consumed. For paths longer than 1 pipe, you can use high capacity for all the pipes except the ones directly before the chest. You can even make the pipe lengths a bit unbalanced, because the pathfinding algorithm will prioritize looking at all the high-bandwidth pipes before the low bandwidth pipes, due to their lower pathfinding cost:
