The Pilot under LIFUS should be allowed to fly only one Type until completion of LIFUS. Some operators allow flying of 2 Types after LIFUS + eg. 100 hours on Type that he can be considered as experienced Crew Member. But to no exactly you should read in the OM-A of the Operator or ask the NFPO, do know exactly.

According to ORO.FC.220
(b) Once an operator conversion course has been commenced, the flight crew member shall not be assigned to flying duties on another type or class of aircraft until the course is completed or terminated. Crew members operating only performance class B aeroplanes may be assigned to flights on other types of performance class B aeroplanes during conversion courses to the extent necessary to maintain the operation. Crew members may be assigned to flights on single-engined helicopters during an operator conversion course on a single-engined helicopter, provided that the training is unaffected.

HOWEVER

When you talk about LIFUS it implies, that the OPC has been done (and has been passed) and as such conversion TRAINING has ended (see ORO.FC.220 (d)(1) ). There are no other objections as ORO.FC.220 concerns a FCM during the conversion training.