Can I install Mojave on boot drive and still keep Catalina running
I have a new MacBook Pro running Catalina.

macs require you to run whatever macOS was shipped with the machine or a latter macOS.  So, you bought a new mac that came pre-installed with Catalina which means you cannot run Mojave on it.  You could get a virtual machine and run Mojave in the virtual machine.  You can get Parallels and run Mojave.  You can try the free virtual box, but expect some difficulties install macos.

If you are still in the free return period, you can return your machine. Look for a new machine with mojave on it.