I'd put in a larger sump basin, two 3/4HP pumps side by side (one higher than the other as a backup) with a 2" pipe extending from each pump and a silent check value on each pipe. I'd prefer that each pump had its own 2" discharge pipe running all the way to the discharge point, in this case. What happens if the main pipe failed and neither pipe could pump anything? If each had its own pipe, at least one would still be working. In a super flow environment like this, I'd be more concerned about pipe failure, too. They had 3 feet of water in the basement with a pump that was at least pumping some water, even if flooding did occur. If both pumps ran to the same 4" pipe would that be needed and that pipe failed, they would both just cycle water. That flood might fill the entire basement. Plus, that 4" pipe is crazy expensive to run as a single pipe.
In that second photo, the current pipe is making two 90-degree turns before it even goes vertical very far, then no doubt at least one more 90 degree to turn horizontal to go to the discharge point. The pump is having to work even harder to pump around three 90 degree corners before even getting to the discharge point. Who knows how many feet of pipe it is going through, as well...if a long distance, it stresses the pump even more. While it will still pump the water, I prefer to use 45 degree angles to make it easier for the pumps to not have to go around 90 degree corners.
I'm not a big fan of stacking pumps...I once saw the result of someone who stacked them and it wasn't very functional looking.
After examining the photo of that current pump, that very much looks like a Zoeller pump. They're usually green and have that metal handle and white float design. The "Super Sump" label on the basin gives it away, however.
http://www.basementsystems.com/sump-pump/supersump.html That is some kind of installed system that someone had put in, of course.
It all comes down to what model pump that is. On their site, they have a dual pump kit that uses a 1/3HP and a 1/2HP in combination, so I reason that they may have put in a 1/2HP. That's simply not enough and it is likely an old pump, so that combination is horrible.
Assuming that your pipe has a 10ft head, if that's a 1/3HP Zoeller, you're only pumping about 35 gallons per minute at the most. If it is a 1/2HP, it might be around 50-60GPM. Out of curiosity, how long have you lived there? Has it always been that way? They botched that install. Check to see if you can use a phone or something to take photos and find the stainless steel ID tag on it.
That flow pipe into the sump basin, by itself, is probably what...4"? That could unleash an enormous amount of water during rare flood events. Normally for regular drainage in a typical residential home, those 4" drain pipes leading to the sump don't fill up all the way. They might reach maybe halfway. With a creek that size beside you, it isn't unreasonable to assume that it couldn't at some point reach full capacity coming through that pipe. Then there's the other crock thing that you mentioned before. I thought I saw a second black "pipe" in the first photo, but it was actually the leg of the nearby shelf that I was seeing and it wasn't that visible on my phone when I saw it. Do you have a photo of the crock that you're referring to?
Until we find out the size of the pump and an approximate flow of water, I'm still going to hold steady that the discharge pipe is too small, there is no check valve at all on the pipe (half or more of that sump basin may be filling back up just from the backflow out of the pipe alone), there is only one pump and no backup at all, and the one pump that is there may not have a high pumping capacity. If that proves to be true, a new larger basin, a couple of high capacity pumps and a larger pipe should solve the flooding problem. A back power system would still be needed to prevent an imminent fail someday. If that creek ever rises to the point where it is actually touching and surrounding the basement, I'm not sure that there are any pumping systems that could keep up. You need some kind of built-up bank beside the creek to keep the water at bay, but dirt erodes in what would be swift water if that happened. I can't believe that they left that land flat like that. But then again, yes I can. Not too long ago, a news station covered a story about a company that built a subdivision of houses that are all sitting on a very high water table. Their sump pumps run 24/7 every few minutes just to keep their basement dry, and the survey papers distinctly instructed the builders that it was not advisable to put a basement in the houses. They did it anyway. Builders don't care nowadays. Looks like a newer house that you have there, as well.
Anything that you do outside without a proper company or permit will likely be illegal per the city. Things like building the bank up, for instance. You could build the bank up, but dirt will erode away when it rises during a flood event and has swift water. Even if you had the money, you could build a wall...but to where, exactly? It runs all the way down in both directions. Build one in front of your property and it will just flow up onto the land way behind the wall before it even reaches the area where your wall is. Waterproofing all that you can might help with the basic water flows, but this unfortunately one of those problems without an easy fix. Elevating that house at least 8 feet (as a builder suggested to me would be the only real solution other than moving) would probably cost $40,000. I know that you don't have that kind of money to throw to the wind, so pumps are about the only option.
One more word of advice: I do hope you have very good flood insurance that covers the entire house, just in case. I would never trust a creek and would honestly install some sort of (covered from rainfall) water alarms along the back of your house and/or in the basement at certain depths. Something to alert you and your family audibly to leave immediately if that creek comes up too high during a freak weather system. You never know when those can strike and they take everyone by surprise. Trying to waterproof it and install pumps and such is fine to do, and we'll be happy to help with any info that we can on that. We never win against nature, however. It could be in the middle of the night during a storm system when you're sleeping and you wouldn't know that a massive flash flood was about to take the house away and that the creek was flooding all the way up to the house and extending beyond it. So I'd figure out a way to monitor that in case such an event ever happens.
As an example, I live in the big city near Atlanta, Georgia. We have a major "stream" (can't believe they call it that) in another part of the city that flows for dozens of miles into other branches of water. Base flow for the stream is only about 67 cubic feet per second and about 3 feet during a typical day without rain. Flood stage is 17 feet. A stream gauge was installed in 1912. In 1919, it reached a flow of 21,000 cubic feet (160,000 gallons) per second and hit 26 feet. A 1" rainfall dumps 1.5 billion gallons of water into the local area. In 2004, it reached nearly 23 feet and was flowing at over 100,000 gallons per second. That typically 45 feet wide "stream" turned into 450 feet wide. It went so high that it washed its own flood gauge away at ten times the normal width, three times the normal speed and 300 times the normal flow. That gauge had been there for about 92 years, hence why a lot of people are always joking about preparing for the "100 year storm." You never know when that time will come. There have been smaller, but almost similar floods in various years since they have started monitored it. While that isn't really relevant for the area that you live in, it goes to show that every so often there are storms that are so unpredictable that they raise even the smaller creeks to devastating levels. That creek in your photo worries me just looking at it, and quite frankly, I'd be trying to find a way to move the heck out of there as soon as possible. It is way too close to the house and they should have never built the house there. There is no cost for life. I have seen floods of creeks and rivers where people's entire houses have washed away with them in it. They trusted the creek too much to not rise up and an above-normal rain event took them by surprise.