First need to know a few things:
1. What is the capacity of the well (gallons per day) in the summer?
2. What is the capacity of the pump (gallons per minute)? What make/model/flow/pressure capability?
3. What is the pressure that the pump can deliver at the pump house?
4. What is the pressure delivered to your house?
5. How do you share water equitably and responsibly with the other party on the well? You might want to put in water meters at about $60 each.
6. What are the differences in elevation between the two users? Who is higher and by how much?
7. How much water do you use? Meter would help determine this.
a. in peak 10 minutes (will determine size of pressure tank)
b. in peak one hour (with 2 and 5, will determine if you need a storage tank)
c. in one day (with 1, 2, and 5, will determine size of storage tank, if needed)
If you have enough pressure at your house (say 50 psi), and the pump will meet your 10 minute GPM demand, you can probably get by with a large pressure tank at your house.
If you have sharing problem, your pressure loss could be because your partner on the line has turned on his pump at his house. He could suck the pressure down so you won't get any water. It could also be a safety issue if he has a pump that is creating a vacuum on the pipe. If you put in a pump and he has none, you could suck him dry.
The best and safest solution to pressure problems would be to install a pump at the pump house that will provide enough pressure for both of you. If you need storage tanks anyway, you will need pumps at the houses, so you may want to keep the existing pump and both use tanks. It will work as long as you don't put a pump on the end of the line from the well.
With the information listed above, and a little engineering, you can have an equitable system for both. If you each try to pump water out of the system as it is, you will take turns sucking the other dry and risk contamination if there is a leak in the pipe to your house.