Unfortunately, no.
I would like it if there was one by Dregal's enchanting stand in Broken Valley that could only hold ores and minerals, and one in the mill basement that held only plants, but there isn't.
The only way to have more storage space pre-tower is to spend skill points increasing the size of your backpack, instead of on useful skills.
Basically, I suggest you avoid picking up any plants and minerals that you don't IMMEDIATELY have a use for, that should help.
