Some features may work fine between them with the right settings. and it shouldn't hurt your system to try (there should be no lasting ill effects after one or the other is uninstalled)
Just note the menu's themselves wont somehow 'merge' but you can probably set it up where one hotkey opens start10 and another classic shell. (or clicking the start button for classic shell, and windows key for start10 ect)
http://www.classicshell.net/forum/viewtopic.php?f=7&t=2399contains a (possibly outdated) comparison between various start menu programs.
If you already purchased start10; you might want to be careful with uninstall to preserve your license.. (I dont know for start10 specifically, but some programs can only be installed 1-3 times with the same license key)