Enter Iaeptus - A million man mission born on a fleet of ten thousand ship to the outer solar system. Their commander : Minevera, a brain-in-a-vat super computer. With a weight of 5 tons, a neuron density 12 times that of mortal man, and 3.4 x 10^25 synapses, it is the most powerful computational device to exist in the Solar System. Their mission: Construct the Atlas Prime, the soon to be largest Spacecraft in human history. An enormous, self propelled gravity tug and inertia thief , it will be built to modify the orbits of Trans-Neptunian and Kuiper-Belt objects.
Since bigger is better for a gravity tug, just how massive can Atlas Prime be?
It Must be self propelled
It's propulsion system must be demonstratably possible
the name of the drive may not contain the words "worm" or "warp"
the mass payload must make up ~50% or more of the sum mass (if possible)
the craft must be able to accelerate to at least 1.0 m/s^2
Given these specs, what is the upper limit on the mass of Atlas Prime?
For clarification, I am asking, given the parameters, what drive will propel the most mass, and what that most would be
Atlas prime is liable to be anything from an O'Neil cylinder to and mass of lead with a rocket strapped to it. The most important part of Atlas Prime is it being portable mass