My standard answer to this problem is to learn how to index trade, and/or trade binary options. As an index or binary options trader you can make as many trades as you want with just a couple grand in your account (just a couple hundred will work for binary options trading). Personally, I like trading an index MUCH better than picking stocks anyway, so it is a no-brainer!
With stock trading you have to do a LOT more work (or at least should be doing a lot more). To find the companies you want to own you need to do quite a bit of research. If you want to short those companies (which most stock traders never do) you need to do even more. Your fundamental analysis should include P/E ratios, company financials, SEC filings, and much more.
You probably want to know what the company insiders are doing, see the big transactions, and find out who the big players are (all of which you can find with free online tools, but you still have to do the work).
As index or binary options traders we don't have to worry about any of that. We just pull up a chart and when the timing is right, we make our play. We can do that as many times as we want each day, and we don't have to be worried about being labeled day traders! We can short the market just as easy (down moves are my favorite) as we can ride it up.
If you are determined to trade stock, but want to get around the issue, then you are going to need to have more than one stock account. You will have to know what each brokers limits are before they label you a day trader. Then simply don't go over those limits.
If you don't like the idea of setting several accounts, you might want to learn how to trade binary options on stocks. Binary options are such a simple way to invest that many traders are flocking to them.
Binary options are not controlled by Wall Street - yet. They offer a nice alternative for many types of investments. The learning curve is small for binary options. You just need a simple binary options course that can have you up and running quickly. No matter what type of investment you plan to try, just keep it simple. When you fully understand the investment (which is much easier to do when you keep it simple), you will normally do better with it!