Sure, it's possible, but good luck getting funding.
Doing research for profit is very tricky, which is why it almost inevitably winds up being done at a loss. The world is full of entities (such as universities and government labs) which would love to be able to do research at a profit, but they succeed only sporadically despite the advantages of lots of smart people and equipment.
The sort of research that can turn a profit is usually fairly incremental stuff (e.g. let's formulate a new kind of paint), and is done within large companies' own research labs with deep domain expertise and trade secrets you won't be able to get your hands on. You can try to invent an improved paint and licence it to DuPont if you like, but if they want it they'll probably have got there before you.
Bluer-sky stuff, on the other hand, takes really long timescales and large numbers of people, with low probability of success. You'll be competing against university researchers in the same field who aren't even patenting their work.
There is money to be made in the last mile -- taking technologies from the point where they're almost ready to hit the market, doing that little bit of extra research to bring them to market, patenting your method and watching the bucks roll in. But opportunities like that are rare and heavily sought after, and even then it usually involves a crapload of money and risk. You can build a startup around just one of these ideas if you can find one, but nobody will give you money to go around looking for them in general, just like nobody will invest in your gold mine until you've actually found some gold.