What board do you have, and what parts of the “base” design do you want. These 3 base designs have differences. Z1/Z2 are similar and are Zynq designs. There are a few differences in the ZCU104 and it is for a Zynq Ultrascale+.
You can find instructions to rebuild the base design here:
Base Overlay — Python productivity for Zynq (Pynq).
At a minimum you need to change the board/device and the pins constraints.
There is a tutorial on rebuilding the base overlay here:
https://discuss.pynq.io/t/tutorial-rebuilding-the-pynq-base-overlay-pynq-v2-6/1993?u=cathalmccabe
Cathal