The answer to this is always "one more"... but if I waited until enough playtests were completed, I'd never get things done. Perfect is the enemy of good.
I usually try to test my games at least three times. Write, initial private testing (either running through the mechanisms myself, or spitballing with one or two others), then rewrite or refine. Second test is usually done in a more formal game set up, among friends or perhaps online. With the feedback from that wider community, a second revision is done. If I had the resources, here's where I'd add in more tests and refinements. Instead the final test is usually done at a convention, with random strangers playing the game... I'd love to get blind playtesting happening with strangers both running and playing things, but if anyone has a reliable way to get that happening I really want to hear it.
Usually, by this stage, I either put the game aside, letting it sit and mature for a while, or start working on layout.