Update: See the other answer by @raconteur below for a correction. You can do what you're asking about doing, but there are no standard processes by which it is accomplished, so you'd need to either research and establish the process yourself or discover and select from relevant processes perhaps offered online somewhere. My answer below is technically incorrect. An operating system can install another operating system onto a disk it possesses.
No, you can't do that. The current operating system cannot install another operating system onto a disk it possesses. You're going to need to install a disk in your system and, without mounting it in your current operating system, boot from a USB or other installation media and install the new operating system to the new disk, being careful not to overwrite data on the current operating system's disk.
Make sense? You're trying to do what's called dual-booting, which is running two operating systems independently on the same system. With this configuration, you can only run one operating system at a time. If you want to run one operating system within another, you have to install a hypervisor and other virtualization apparatus to allow two operating systems to share the hardware simultaneously.
If you can tell me your preference, I will be glad to point you to some documentation.
I agree it sure would be nice to be able to run Anaconda as a standalone app and install to second disk. I can't believe no one has ever added that mode to the installer in all these years. You and I can't be the only ones who want to do this.