Yes, you can do this. Yes, it's tricky because when you add songs initially, it appears songs can only be added to one group. But there is a way to do it.
I use PIL to DJ weddings. All of my music is sorted by decade and tempo. But I have 3 additional track groups specific to each wedding: must play; nice to have; and do not play. After each wedding, I clean out these 3 groups and replace them with the requests the couple made for my next wedding. But the tracks stay in their original track groups as well.
Top Menu > Manage > Track Groups
Find your "destination" group and double-click on it (or single-click and then click the "Edit" button).
Now, you'll see a window with 2 columns. On the RIGHT is every track currently in that group. On the LEFT is your entire library, minus the tracks on the right.
If you want to add tracks to this group, find them on the left (either manually or by using the search field above it). Then select the track(s) you want to add to the group, and press the ">" button to move those tracks over to the right. Once you hit OK on this window AND you hit OK or Apply on the Track Groups window, your changes are done. The track(s) you selected should now appear under both their "original" track group and the new one.
Likewise, if you want to REMOVE tracks from a group (for example, a CHR station is likely replacing some of its "Currents" weekly), it's a similar process. Open the Track Group you want to remove things from. Find the track(s) you want to remove on the RIGHT side of the window, then click the "<" button. Again, click OK to close the group editor, then OK or Apply on the track group list window, and your changes are saved.
I am trying to figure this out as well. I have a station that plays mostly classic country but also plays pop songs for a couple of hours and some of those I want to list in both pop and country