The act of continuing to date a girl you want to break up with while you start dating a new girl. It usually occurs because you either don't't know how to break up with your girlfriend, or because you want insurance in case the new girlfriend doesn't work out. The period of overlap is like the way shingles overlap on a roof.
John's was shingling with Alice until he finds a way to break up with Mary.
"Fuck me, Bob's shinging again!" said I, to Shay, as Big Bob bellowed out the lyrics to Deep Purple's "Smoke On The Water", as he does to every fucking song of every fucking genre! I continued, "He's fucking tone deaf, that cunt!"