Strange as it might sound the answer is YES. An on-loan player can be loaned out to another Club. Needless to say with the consent of the parent club.
Take for example in 2017 Leicester City signed Mali international Molla Wague on loan from Udinese, where he was on loan from Spanish club Granada.
How is it possible for a loan player to be loaned out to another club?
Loaning out an on loan player is possible because any loan spell lasting a season or more is registered as a permanent transfer by football governing body, Fifa.
Prior to this loan move, Wague had been sent on a three-year loan to Italian club Udinese by his Spanish parent club, Granada, in 2014.
Wague did not make a single appearance for Leicester City during his loan spell.