Does the gravitational force of one object interfere with that of another? Assume we have two iron spheres, Sphere A and Sphere B, with identical masses floating in the vacuum of interstellar space separated by some distance from each other.  The gravitational force of each sphere pulls on the other sphere equally.
Now assume that a third identical sphere, Sphere C, is placed in between Spheres A and B.  I don't know that it matters where it is placed, but let's say it is place exactly at the mid-point between A and B.
Does Sphere C have any effect of on the gravitational force between A and B?  Is there any kind of mass, gravitational or even EM interference that changes the gravitational force between A and B with the addition of C?  I understand that C now has it's own gravitational force pulling on both A and B (and vice versa), but I'm more interested in any interfering effects between A and B caused by C.
Thanks much and I hope this makes sense.  I could not find the same question asked previously.
 A: 
Does Sphere C have any effect of on the gravitational force between A and B?

Nope. C does not make any difference to the force between A and B, but its introduction has the effect that the net force on A has contributions from both B and C. (Likewise for the other spheres too.) This is because gravitation obeys the principle of superposition. 

Is there any kind of mass, gravitational or even EM interference that changes the gravitational force between A and B with the addition of C?

Nope again. The gravitational force between A and B only depends on the masses and the relative separation of A and B. Any extra force arising due to whatsoever reasons, shall add to this force, and ensure that the net force on either of the two comes out to be different. But it does not affect the "gravitational force between A and B". 
However, the above is how Physics works here, but there is certainly a possibility of some play of words here. Let us say sphere C is electrically charged negatively, and so is A. Ignoring the induction of charges as a first approximation, the extra element in the story is that A and C repel each other now, in addition to the gravitational attraction. So, the net force on A has both positive and negative contributions, and you can have a play of words argument, that this EM force has, so to speak, screened the gravitational attraction. (Of course, in general, the EM force contribution shall be a lot larger, for usual charges and masses.) But notice that this argument only concerns the net force on A (or B), and not the "gravitational attraction between A and B", which is still unaffected by these factors. 
A: The sphere will stay in-between because net force is zero. However, the spheres will all lump together on sphere C because while C will not move, A and B will.
