Is it possible to queue songs to play next while the current song is playing?
Have a look at Juke Box. That might do the job. I've not used it but I believe it has to be set up in advance and doesn't work on the fly.
It's also possible to load multiple instances of BIAB. This would let you have one playing and a couple waiting.
As Noel mentioned, Juke Box might be the best way. It can load and play an entire folder of songs, with filters to only play specific types. Just make a new folder and copy the songs you want played into that folder.
It will play songs in alphabetical order, or you can choose random playback (which will also avoid playing any song twice).
Check out the Juke Box options for more detail.