Yes, you may be able to increase the flow rate but it all depends on a lot of factors. You may also be able to drill in the vincinity and get a much better flow since you apparently have a confined layer putting pressure on your aquifer.
Your best bet is to consult with a well driller in your area that knows his stuff and not just what so and so says on here. No offense to anyone on here but there are a lot of misconceptions on springs, artesian wells, flowing artesian wells, recharge etc. A good number of wives tale mixed in.
There are maps out there showing where confined layers and potential flowing artesian wells are too. And many times you can even consult with a state geologist at no charge. I found one on the Internet for my area and he was more than happy to answer questions.
I have a friend that raises trout like I do, and he has put in two wells through a confined layer of limestone and gets more than he needs. Each well puts out 500 gallons a minute. Interesting thing is if he moved over just a few feet he would get much less.
