SpaceX is all about getting into Earth orbit. It has no capacity or projects to go beyond there at present. Elon Musk has expressed a desire to do such things, but the company is not yet engaged with them. Doing so would likely involve fresh investment (for much larger amounts of money) and revaluation.

Earth orbit is hard in terms of energy costs, but relatively easy in other terms: you don't need to solve the long-term independent life support problem, manufacture things off-planet, or figure out how to do supply lines in space.