Short answer: No I don't move stops to breakeven!
Long answer: I never ever move my initial stop loss before a trade hits my R-multiple threshold. However this is mainly due to my sharp stops. If you use wider stops it might make sense to sell on a proper red flag before hitting the R-multiple threshold. But in my honest opinion it is better to avoid any intervention after the entry thus allowing the market to do the magic for you!
I do use scale-outs to avoid being shaken out on natural pullbacks which more often than not coincide with stocks hitting the widely followed 3R mark from widely followed entries such as pivot breakouts and pocket pivots. Once I scaled out the initial stop loss becomes meaningless and I will trail it up to the next logical level of support. However this is a just a safety mechanism for protecting me against a flash crash as I will sell on a proper red flag independent on the "trailing" stop. Also be aware that such a protection trailing stop must be placed ABOVE support so that you are getting filled before all the other stops in the case of a sudden crash. This is the exact opposite to a regular stop loss, which must be placed below PLL support in order to avoid regular shakeouts. A protection trailing stop is just an intraday protection mechanism when you are not sitting in front of the computer.