I'm playing in a single-player survival world on Bedrock Edition on my Xbox One and I've been looking at some of the item-sorting builds on YT. I'm currently leaning towards the design shown in Minecraft Tutorial - Compact Automatic Item Sorter - Expandable(Minecraft 1.14+), but I have a couple of questions before I start "wasting" resources. The main one at this time is, is it possible to have an "overflow" for a single, sorted item? Or, to ask it another way (based on the only idea I've been able to come up with so far), will a hopper in this kind of system drop items to a lower hopper when it's connected chest is full?
For example, let's say I build an item sorter with one chest that's for cobblestone. I'm going mining, and I obviously get a LOT of cobblestone blocks, so every time I come up for air, I start throwing all of them into my sorter. The machine works flawlessly and starts dropping the cobblestone blocks into the appropriately designated double chest. However, that chest is pretty quickly completely full. I'd like to be able to have a second chest, and possibly a third (or more) stacked vertically so that once the first chest is full, it goes ahead and moves on to the second, then third, etc.
I imagine this sort of "overflow" design would probably require the second and subsequent chests to be below the first, although the best way, IMO, would be to start filling from the bottom up instead of from the top down. I think I may have an idea of how to accomplish the latter, but I'm still a relative Minecraft noob. I've not yet gotten to the point of making my own designs or making any major, functional modifications to the designs of others. I'm trying to teach myself how to make use of redstone for these kinds of machines, but I have a lot yet to learn.