Can I downgrade (put earlier version on) OS on late 2013 iMac 27 inch?

Downgrading the Mac from OS Catalina to El Capitan is quite a step backward.

To do so will require you to reformat the startup drive, resulting in the loss of ALL DATA on that drive. After which you will need to reinstall macOS El Capitan from either: 1) a bootable installer or 2) a previous El Capitan Time Machine backup or maybe 3) Reinstall from Recovery partition.

Please see > How to create a bootable installer for macOS - Apple Support

also > How to reinstall macOS - Apple Support

In addition the 2013 will need to backed up using a bootable clone, you cannot use Time Machine as you cannot restore from Catalina backwards. If you have a bootable clone of Catalina, then at least you can dual boot AND copy and paste the files you want.

👍🏽