try looking under water tower

Here is a link that might be useful: water tower

Your idea is workable. It will be necessary to cycle the well pump at intervals that will not empty the well and have that pump running while dry which will ruin the pump. Your capital outlay will be considerable and operating costs will be considerably higher with two pumps. Some sources indicate that the typical household uses about 200 gallons per day, obviously not all at once, so your present system may work well enough as it is. An alternative is to deepen the existing well. We are not told the size (diameter) of the existing well. A 6" well holds about 1 1/2 gallons per foot of water depth, so an extra 100 feet would store about 150 gallons. Additionally, while that is being exhausted, more is coming in at the rate of a gallon per minute. I have a well 610 feet deep with an inflow of 1 gallon per minute, static level of about 70 feet. At times it has supplied 5 households without problems.
For deeper and at replacement, I suggest a 240 volt pump. For a given horsepower, the voltage drop in the conductors will be just 1/4 that of the 120 volt system.

Two questions come to mind. Won't water in the storage tank support microbial growth? If so, what needs to be done about that? Isn't 2000 gallons a awful lot for one typical house if bus_driver's number is correct and a typical household uses 200 gallons/day?

Why not install a larger pressure tank and a slow pump?

"Won't water in the storage tank support microbial growth?"
A good question. But consider that the water in the well is just sitting there until some portion of it is pumped out. The pump is often considerably below the surface of the water. I suspect that much of the "microbial growth", if any, is simply not harmful to people. And it would be as prevalent in the well as in the tank. I have lived much of my life on untested and untreated well water- including several years when the water was drawn up with a bucket and rope.
My wife's Mother is approaching her 100th birthday and never had any water supply other than a spring or a well. Her water supply comes from my well now. And wisely or not, this well has not been tested.

This post was edited by bus_driver on Tue, Dec 4, 12 at 21:35

Bus_driver, all good points. I thought of most of that and shrugged. Not being a well or pump expert, I can't really comment beyond the fact that a lot changes after the water if pumped out of an open or closed well. Important changes that I can think of are temperature, dissolved gasses and exposure to surface contamination.. With a pressure tank, the dissolved gasses and exposure to surface contamination won't change much until the water hits the faucets. In an open tank, it will. If I were contemplating a change like the OP, I would do considerable research on the conventions involved in construction and use of such a cistern.

People in NZ and Australia use tank water, collected from rainwater exclusively in some places.

Theoretically, it should probably be treated and the tanks cleaned periodically, in practice, few do and they're fine.

They've done a lot to improve the water going in, with diverter systems that allow the eavestrough to be rinsed out before the water goes into the tank, things like that.

Presumably OP is in a climate where freezing won't be an issue.

I was once employed as a private water treatment specialist and solved a very similar, even worse problem.

Flow was just under 2gals/min, and well pumped down in 11-12 minutes.

Installed 2000gallon holding tank, influent (supply to holding tank) treated with chlorine injection - to allow required contact time for sanitation. Pumped from holding tank with Grundfos QD(?)35 110volt, inline aeration venturi, then through a 20" carbon block filter to remove the chlorine.

As far as the well pumping down in 11 minutes, it then would take 3-4 minutes for the well volume to return.. I solved with an electric timer (like ones used for electric water heaters, but found one with a pin for each minute. Set it to feed power to the pressure switch for 10 minutes, then cut power to the pressure switch for 4 minutes.

A float switch inside the tank killed the pressure switch as well.

Surface contamination has already occurred down the well, this is why we sanitize wells and plumbing systems, through to all the points of use, with chlorine from time to time. Also, holding tanks are not "open tanks", they are very closed - in fact, they even have a screw on 18" cap. An open tank would have just vented off the chlorine, nixing any sanitization; requiring chlorine injection AFTER the holding tank.

Has worked great for 7 years now with minimal maintenance,

Also should note that it supplies water to a 4 bedroom, 5 bath, fully occupied home for family of 7.

Is there a nearby pond or other water source for fire fighting?

But consider that the water in the well is just sitting there until some portion of it is pumped out.

Yes; but it's underground where it's not exposed to air, which is needed for microbiral growth. And 80' seems like a really, really shallow well.