Oh, I'm happy to respond, but grab a coffee, because this is going to get long.
Background: During the flood of 2013, we had two separate instances of 5" of rain in a 36 hour period. And we live in central Michigan, which is basically swampland anyway.
As we worked to pump the 4" of water out of the basement, we started learning all sorts of fun things about our house. The home has exterior drain tile in the back, but because the dwelling is older (1958 construction), the drain tile is clay and is likely crushed to bits. Said tile is connected to a deep pit that's emptied by an external sump pump. The sump pump failed, which only exacerbated our problems. We couldn't snake the drain tile, and so we figured most of the system was a bust. Cost of new exterior drain tile? $12,000. Scratch that.
We were having problems with water entering from the front side of the home near the sewage line as well. We figured water was pooling in the trench and coming into the house at its lowest point. There's no drain exterior tile on that side of the house, and so we needed something to deal with the rising ground water in the front. We sunk an interior sump pump at the lowest point in the front. We were banking on tying the new sump pump to the interior drain tile near the foundation (shown on the original drawings, I swear!), but the tile didn't exist :( Ugh, we totally got screwed by some old builders who decided to cut corners. The sump pump used to eject into the front yard, which did us no favors (water just came right back in), and so we dug a trench around the house that empties into the creek behind us. The sump + trench digging set us back a good $6000.
We also had no gutters on the front of the house. I suppose the architect figured the expansive eaves (beautiful, I might add) would be enough. So we put gutters on the front of the house and tied them into the same trench that takes the water to the back of the house. Oof. Gutters aren't cheap, either.
We replaced the dead sump pump in the back, and the new one is quite active. This leads me to believe the exterior drain tile is still somewhat functional. That's the good news, I suppose. Our internal sump goes off every few minutes when it's raining hard, but we have no indication that it's not able to pump out all the water rising under the floor; we were worried that it would only reduce the water pressure within a certain radius. I don't think the recent rains were quite heavy enough to conclude that we're "safe," but we feel better than we did last April.
My questions to the OP:
Do you have drainage tile? Is it connected to the sump? Or is the sump just a hole in the floor with a pump in it?
Can you consider working on the outside of the home? can you dig around the foundation and waterproof with drain tile?
There are many options, and they run the gamut from affordable (clean your gutters and drain tile!) to super expensive (excavate your foundation or dig up your whole floor).