This goes for the Web-interface only. The Subsonic android app do not have this problem.
After you have selected a playlist, you can click on Play in the top button row for the playlist. This will play this playlist instead of the currently played tracks.
However, there is no way to Add the new playlist to the end of the currently played tracks. - Currently you can add all tracks in the selected playlist to the currently played tracks by using the + button located before each song in the selected playlist, but it is tedious to do for long playlists.
What I try to do is to make separate playlists for each of my favorite artists and then add three or four such playlists to the current played playlist, for then to shuffle the resulting playlist to get a nice temporary playlist with a shuffled play of the favorite tracks for some of my favorite artists. The point is that i do not want to save that playlist since I will do the same over again the next time I play this, so that i can pick up newly added tracks to the other playlists.
On the android Subsonic app I can do this just fine, but I cannot do it in the web interface on my computer.