When two objects are near each other how would increasing one object's mass affect the other object?

When two objects are near each other how would increasing one object's mass affect the other object?
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The other object would be drawn more strongly to the one with increased mass. But whether that influenced their motion would depend on the actual forces involved. Since gravity is a "mutual" attraction, the effect on the two-object system could vary in ways other than the increased net attraction.
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