Does this exist?
There are a few aspects you need to consider.
First, there is a difference between order types offered by your broker and order types offered by the exchange.
If an order type is offered by the exchange, it means that the order can be delivered as such to the exchange and will be executed from the exchange systems directly.
For all other order types, you or the broker has to simulate them. This means that only that portion of the order that is supported by the exchange gets transferred there, the rest happens on the systems of the broker.
Simple example: the exchange supports only MKT and LMT but no stop orders. So, in case of a stop limit order, the order would stay on the broker's system until the stop was reached, then the limit order would be transferred to the exchange for execution.
There is one important caveat here: an exchange might not only not support certain order, they might outright forbid them.
Why is all of this relevant for you? Because even if your broker would not offer the kind of order you seek (which would usually be called conditional stop or adjustable stop order, or similar), many online brokers allow you to create your own algorithms (either within their own software, via API control, or using third party software such as MetaTrader). You just have to make sure your algorithm wouldn't create (detectable) orders which are not allowed by the exchange.
Does this make sense?
Sure it does. Is it a sure fire way to be profitable, though? No, it's not.