Supposing there is a system of several (four to twelve) celestial bodies which are orbiting a star. In this system of bodies, each body is similar enough in size that no single body has a dominant gravitational field. These objects lie in overlapping and fairly close orbits as well. Naturally, this system of planets would be very unstable and would inevitably collide together or sling each other out of the system. However, my main question is: How fast would this likely happen and could it happen slowly enough to be found in something other than a brand new solar system?
A few possible answers to this question that I can foresee would be for it to take several thousand years for these orbits to decay or perhaps several hundred thousand years, though I am unsure if these are accurate estimates. It would be interesting to perhaps even colonize one of those bodies and have the resulting society go through several iterations of civilization in the time it takes the system to fully collapses.
Now, to make sure that I'm being clear, I am NOT looking for a functional model of a multiple-body system with predictions of all possible futures. I am instead looking for a general estimate of the maximum time an unstable system might be able to exist without orbits collapsing.