Griffiths wants to take advantage of Melbourne's good weather as he feels Enxuto is not as effective on soft ground as he is on firm footing.
"He's never been a fantastic rap on wet ground, so at some stage he will bypass the winter, and then he may be able to take that next step in the late spring, going into summer," Griffiths said.
"I think there is more in him, the question is whether he can do it right now."
While not wanting to look too far ahead, Griffiths said there was a couple of options coming up depending on Enxuto's performance on Saturday.
The Listed City Of Adelaide Handicap (1500m) at Morphettville and the Listed Golden Mile (1600m) at Bendigo, both on April 12, could come under consideration.
"If does go well on Saturday, then the natural progression would be the Golden Mile," Griffiths said.
"But the Adelaide race could also be suitable.
"This run will be a bit of a fork in the road as to how far we go this campaign."