As far as I've been able to tell, you need board certification in internal medicine to due medicine subspecialties such as cardiology, gastroenterology, heme/onc, endocrine, etc. Family practice usually gets 1 1/2 year or less training in adult medicine and its subspecialties due to their required pediatrics and OB rotations. There are very few fellowships from family med, the only ones I know of are sports med and gerontology as mentioned by a previous poster.
Although it may be possible to work out a special deal, I think it would be very difficult because program will have plenty of better qualified medicine residents to choose from, especially in Cards and GI.
The other option if you're thinking of family practice but aren't sure if you want to subspecialize is to do Med/Peds, which is four years. That way you can do medicine or peds subspecialties. Good luck