Let's say that there's a stock I am investing in. Market price is currently at $300. The market is rallying and I would like to sell if it reaches $315. Great, I will set a limit order at $315. But here's the thing, if this stock just keeps moving on up, and I sell around ~$315, if the stock rallies to ~$330 and I missed out on a sweet $15 per share and the opportunity to set a higher floor price at which to sell.
What I would want to do is once, and only once I pass a threshold ($315), enable a stop limit order automatically to sell as soon as possible if and only if it falls back down below $315. Essentially, I don't want to bail out of a rally if I don't have to.
Does such an order type exist? Asides from needing the money or other tax implications, why wouldn't you want to do this instead of a classic limit order?