Lest anyone misconstrue my remarks, let me say at the very beginning that I think of Hysys as a truly exceptional simulation product which has pushed the state-of-the-art consistently for many years.
However, the real problem under discussion here is that Hysys does not offer a flowsheet scaling option, as do some other simulators. Ideally, after converging a simulation, the user ought to be able to re-scale the entire problem to match a specified flow for any stream in the flowsheet. In other simulators, this does not require a rerun of the flowsheet, but is handled instead as part of the comprehensive report generation (unit operations and stream properties). Unfortunately, such a report is not generated by Hysys at all.
You may wish to examine your problem and determine which stream flows will need to be scaled to the new flow. Then, try to edge the simulation in a number of discrete steps (I would recommend at least 5, starting first with the amine circulation rate) until you reach the the desired final condition.
An alternative (that I would favor over the one described above) would be to transfer the stream and unit operations summaries to Excel and do the scaling in Excel manually.
By the way, as you scale up, there should be no reason for you to adjust the number of theoretical stages at all, as that changes the problem definition.