I was dropped by Allstate about a month ago, due to three claims I've had within the last five years. I've had a couple of quotes, no less than 1,400 premium a year, with
Foremost. Does anybody know of an insurance company that might be cheaper?

Having had 3 claims in a short period, you're going to have to look to a smaller company which won't necessarily be cheaper. You present a greater risk and until you're a claim-free for a number of years, you will have to suck it up.

Foremost is known for taking on "riskier" policies so they may be your best bet. Most of the larger companies won't touch you with so many claims but check your Yellow Pages for a local company.

Top-line direct writers like Allstate (State Farm, Nationwide) are generally more restrictive on their underwriting than some of the smaller companies. Find a well-regarded independent insurance agent (who writes for several/many companies) in your area.
Bill