Exponential growth doesn't inherently require population expansion. This would especially be true for a far more advanced civilization. You could dramatically amplify your colonization efforts with machines, reducing your need for traditional population expansion (productivity expansion in tandem with population contraction is exactly what we're going to see on Earth this century).
Without population growth you lose the motivation. Communication gets harder every time you add a star to your civilization, unless you somehow break the speed of light. Resource use is unlikely to be a motivator - a civilization sufficiently advanced to be multistellar will no doubt have cracked either fusion or the stain sphere problem.
