Multi-Object Systems 
The linear form of Newton's Second Law when written in terms of momentum implies that it is easily generalized to allow for a system consisting of many objects. Simply add the contributions from all the objects within the system:
It is important to realize that although we are now allowing multiple objects within the system, the relevant impulse to add on the right hand side of Newton's Second Law is still only the external impulse. Impulses applied to one system constituent by another system constituent end up canceling out of the equation by Newton's Third Law.
It is also worth noting that technically the concept of linear momentum applies only to collections of point particles. The momentum of a rigid body, then, must technically be thought of as the sum of the momentum of each of the atoms in the body. This sum turns out to be the body's mass times its center of mass velocity. The momentum of a system composed of many rigid bodies and point particles is then the sum of their individual momenta, which again can be expressed as the total mass of this system times the velocity of the system's center of mass.