I just went downstairs to check: I have fourteen rolls of tape in various states of use, haphazardly stacked in piles and hanging from random protusions, each equally covered in sawdust and many in paint and woodstain. A few of them are repeats: I have no less than four 1" 3M ScotchBlue rolls started, likely because I wasn't able to find them when in the midst of a project. Clearly, I need a better solution. Like this clever solution: a simple cleat-mounted box from American Woodworker. Since most rolls of tape have a few standard internal rings, you can make the axle-blocks in a few sizes and be set for life.
I made my dispenser from scraps of 3/4-in. birch lumber but plywood will work. Almost all regular-size rolls of tape have a 3-in. center hole, so the same size filler block will work for most rolls. I made my filler blocks 2-3/16-in. square and rounded the corners until I got a tight fit inside the roll. The axle was simply a 3/4-in. dowel. The axle fits into a slot in the dividers. I cut the slots on my router table using a 3/4-in.-dia. straight bit. They are 1/4-in. deep and 1-1/2-in. long.
Jumbo Tape Dispenser [American Woodworker]