sump pump basement

Sump pump cannot keep up with very heavy rains - please help

Summary of the situation

I have a 1/2 HP Zoeller Model 98 that discharges 52 gallons of water per minute, but in a torrential downpour that's still not enough and the pump runs non-stop. My vertical sump pit is about 18" wide and about 20-22" deep. I have a walk-up basement with a drain at the bottom with a 1.5" PVC pipe that runs into the sump pit. There are also drain tiles from the foundation which also empty into the pit. The Zoeller 98 is designed to turn on at a water depth of 9.5" and off at a depth of 3". So the pump is discharging 6.5" of water when it runs. With an 18" wide pump I calculate that as 7.16 gallons of water discharged. It takes 8 seconds to discharge through a 1.5" pipe with about 11 feet or rise and 40 feet gravity fed to outside the house. 7 gallons in 8 seconds works out to about 52 gallons per minute. During a heavy rain/thunderstorm, the sump pump will every 30-45 seconds. During extremely heavy torrential rain, the pump cannot keep up and runs non-stop. The water level slowly rises higher in the pit. At a certain point the water level is higher than where the 1.5" PVC pipe from the basement stairwell comes into the pit. This causes the water in the basement stairwell to start slowly backing up in the stairwell. If the rain does not significantly slow down soon enough, the muddy water backing up in the stairwell eventually gets too high in the stairwell and comes into the finished basement through the door, ruining the carpet and making a mess of things. The issue first happened 20 years ago when I had just purchased the home. I had some landscaping done to try and divert the water and that helped a lot. This summer we had a crazy-heavy torrential rain storm and the pump couldn't keep up and ran non-stop. And unfortunately the muddy water backed up in the stairwell and came in through the door just as it had 20 years ago. The water did not overflow the sump pit, but I was watching it and it came within about 2" of the top. This means that all the drain tiles were under water as well, as the pit was almost completely full. I had a couple thousand dollars of landscaping done to get the grading away from the house because with hindsight some areas had settled and I thought that would help decrease the water coming into the pit. Also in recent years there has been a lot of heavy rains and it is said that the underground "water table" is very high. Then just a few weeks ago we had another crazy-heavy torrential rain storm, the first since doing the recent grading work and the first real test to see if it helped. I heard the pump going on and off, on and off and thought it would be OK. But after about 10 minutes of this rain I noticed the pump was running non-stop. And sure enough the water started backing up in the stairwell. Fortunately the rain stopped before the water level in the stairwell could reach the door. I do NOT think the issue is that there is too much rain water coming down the walk-up basement steps, and NOT an issue with the 1.5" PVC pipe being not big enough. During heavy rains I watch the steps and there is no water flowing down it. Also when this problem happens and the water backs up, the water is mud-brown. This suggests to me it is backing up in there, either from the sump pit or perhaps seeping up from the ground. So now the issue is how to properly solve it. I can't figure out how that much water is flowing into the pit. All areas up against the perimeter of the house are raised so that water flows away from it. That said, the backyard does slope down to the house, and will form a 2-3" deep lake (only with very heavy prolonged rains), but the edge of that is still about 15 feet away from the house. There is a neighboring 4" drain pipe that runs behind a hill which helps disperse that water from the temporary "lake". However the 4" isn't big enough so that's what causes the lake. After about 20-30 minutes after the rain stops this lake is gone. Also this lake only comes with the torrential rain, not typical rains. The 4" line cannot be redone to made larger at this point, because it runs through a neighbors yard and under special stone landscaping and they are not willing for me to have it dug up. Ideally I'd like to fix the root cause of the issue - so whatever is causing that much water to get into the pit I'd like to divert it somehow. However I cannot determine where/how all that water is coming from. It is pouring in from the drain tiles - I can see that inside the pit. But I don't know where or how that water is coming up near the foundation to make it flow into the drain tiles in the first place. If I can figure that out, I would love to fix the issue by diverting that water away. However because of the grading I do not think I have many if any options for running french drains and such outside the house. I also don't understand why after nearly 20 years this has become an issue again. As mentioned it happened once 20 years ago, and then nothing until this year where it's already happened twice within a few months. So that said, if I cannot treat the source, I have no other choice I suppose than to treat the symptoms. Which means I need a way to greatly increase the capacity. This likely would mean installing a 2nd pit with a separate discharge line, essentially doubling my capacity to 52 x 2 = 104 gallons per minute. I assume that would be enough - but who really knows what type of capacity I need and whether that would 100% solve the issue. I'm not looking to do this myself, but rather I want to hire professionals. I've had a basement water proofing company that does drain tile and sump work come out, and they don't have any idea where all the water is coming from. They suggested adding a 2nd pit on the other side (front) of the house, but I'm skeptical as I don't even know if that much water is flowing in the drain tile over there - I suspect it is all from the backyard. I've also had a few plumbers out to look at it, and they don't know how all the water is getting into the pit either. Can you guys please make some recommendations on how you would go about trying to best solve this, and what your thoughts are on what may be causing it? I really need to solve this because I know it is only a matter of time until I have water in the basement again if I don't take action soon, and I need the peace of mind not to be so anxious every time a heavy storm rolls in!