Can I use part of one beacon pyramid as part of a second pyramid?
If I want to have more pyramid powers available than a maxed pyramid can provide, I'd have to build a second pyramid. Can that second pyramid be partially made of blocks that are still within the first pyramid?
Yes, according to the Minecraft Wiki page on Beacons:
Adjacent beacons may share blocks in their pyramids, allowing for fairly efficient designs that provide multiple powers.
Here's an example, again from the wiki:
