Proximty due to being in the same star system does not appear to be a defining factor in allowing a stargate to work near another. Rather, the governing factor is the division of stargate-space into discrete regions wherein gates could appear, that is the resolution of the three-dimensional space by the position of the constellations/planets which are represented by the address glyphs.
We know there are c.40 positions in space which are used to define the address, by a simple process of intersection. So, logically, there can only be a finite number of combinations which will yield a valid intersection. Going further, there will be many intersections which will be physically "quite close" on a cosmic scale, say a few hundred million miles, perhaps.
Now, we also now, also from basic astrophysics, that the gate system already has a degree of tolerance in "accuracy" of the intersection - although the glyphs for earth are fixed, its position in space alters by 180 million miles due to orbital and annual rotation etc. Now, this gets worse, because the constellations and planets used to define the intersection are ALSO moving in such a manner!! :dead:
So, we must assume there is a specified tolerance around each "absolute" intersection point, which must be quite large (a few hundred million miles at least). Any time a pair of gates are within that physical distance, they would interact, as for the numerous examples of a second earth gate. But, this is based on physical distance, rather than any specific location such as within a star system.
The converse also holds true: within a sufficiently large star system, two dinstinct addresses could be used that are far enough apart that they produce two locations outside each other's "radius of tolerance" but are still valid. As discussed elsewhere, the point of origin is almost purely symbolic, so can quite easily be different, despite being in the same star system - the two gates on earth have different glyphs for example, though this could be due to wherever the Goa'uld found the second gate before installing it on Earth...
To be honest, thinking about how few glyphs there are, trying to find a SINGLE intersection would be difficult. Imagine spreading forty points about equally around a sphere, and then intersecting three pairs of points so that they intersect within a small volume!