Sure, there is always the possibility that there's more going on with matter and energy than we currently know about. In fact, that's the goal of science -- to understand more about nature, and to find another kind of force would really be a big step in our knowledge.
There are limits to what form such a new kind of force could take, given the large amount of experimental evidence currently available on the forces we know about. We have explored very carefully the reactions of matter and energy on "people-sized" scales of energy and distance. The usual forces of gravity and electricity and magnetism are very apparent on these scales. When we explored what goes on inside atomic nuclei, and how individual particles interact at high energies, the weak and strong nuclear forces were discovered and investigated. We now know that the weak nuclear force and electricity and magnetism are all manifestations of the same interaction. We're still working on how gravity and the strong force fit into the picture.
It could be that at shorter distance scales and at higher energies, there is another kind of force holding stuff together. If the particles we know and love really are made up of smaller pieces that are held together really really tight (so tightly that we would not be able to see the little pieces, only the combinations of them), then an undiscovered kind of force may be at work. There are limits on the size of things like electrons and quarks, and indeed they are quite small. Such a new force would have a very short range, to hold the pieces of particles together but not be noticeable on larger distance scales we can probe.
Alternatively, an undiscovered force could have a very long range but be very weak. Gravity is the weakest force we know of, but if there's something much weaker than gravity it might have escaped our attention. Current cosmological evidence suggests that there is a large amount of "dark energy" in the universe which is speeding up the expansion, but as far as I can tell, it can be included in Einstein's gravitational model and so doesn't need new forces to describe its behavior. But that doesn't mean there aren't any new forces out there, waiting to be discovered.