Each mass has its own gravitational field, and the field strength (gradient of gravitational potential) at any point is the sum of the field strengths at that point from all masses. Apply Newton's universal law of gravitation to each pair of objects to determine the force of attract between them. For one object, add the forces of attraction to each other object to determine the total force on the object. Divide by the object's mass to get its acceleration. So yes; the fields combine by simple addition.