Yes, most definitely.  There are many people who house & pet sit, and a few who will care for your pet in their own home. The fees run an average of $300 pesos a day. There are also companies where sitters register to provide a free service for people looking to have homes and pets cared for while they`re away in exchange for free accommodation. Check out these websites to learn more:
Trusted House Sitters
House Sit Mexico