I have a sump pit (with pump) located at the back corner of my basement which always has water in it and the water level is just shy of the pump activating (and that's about 5 in from overflowing). It turns on about 5 times a day when the water occassionally rises a bit, or some vibration gets the pump to turn on. After emptying, the pump fills right back up. I have a check valve and it's working, and the water empties directly into a municipal drain (not my sewage pipe).
The pit I have is a bit narrow and I believe shallow.
My basement flooded once when we had a very very bad storm and the pump that's been there for years broke. Other than that no problems (fingers are always crossed).
Strangely enough, my neighbor's house (50 ft away) is at about the same height and he doesn't have anywhere near as much water.

Now I am thinking of putting a second pit in, but the plumber is afraid to dig with such a high water table. He recommends first digging the existing one deeper, put the pump lower to drain out more and get the water level lowered.

So my questions:
1) Does the plumber's recommendation make sense. If I have a high water table and dig deeper, the lower pump will run all the time ?
2) Will a second pit help in this case or will I simply now have two pits that fill almost to the top ?
3) Is there anything else I can do - I don't believe this has to do with grading since even when there's no rain, the pit's usually full ?
4) My home is about 15 years old, do I have to worry about my foundation or structural integrity if I have a high water table ?
5) How can I tell if my pit is shallower than "normal" I know I can put a yardstick in to measure, but I thought a pit is actually deeper and there's actually drain tile there ?

Thanks very much in advance...