I do not have any links to offer here, but I have seen some systems that are intended to channel water from all around the perimeter of a basement and into a single sump. Unless you are dealing with a tremendous amount of water or you cannot get it all to run to a single location, I cannot imagine needing more than one pump.
In my own case, I had a leaking wall in the basement with an accumulation of water in one corner, and my son-in-law and I solved that problem by addressing drainage issues outside the house ... specifically, by repairing a disfunctional rain gutter along that side of the house and by re-directing gorund-surface water away from that particular corner altogether. In other words, I would suspect you can at least greatly reduce your problem by doing some work on the outside of the house. But if your basement floor might be too close to the water table for that to truly work -- you had mentioned seepage up through cracks in the floor -- you might look into possibly using a well of some type to extract water from under your basement floor during heavy rainfall. A school here where I happen to live was built in a swampy area, and I have heard there are extraction wells and pumps keeping it dry 24-7-365.