Here's a little thought experiment that shows one possible way in which adding to a winning position CAN BE profitable. It begins by assuming that you posess at least one profitable mechanical trading system which captures large trends lasting several months. (If that assumption is not true, you can disregard the rest). Trading 150-day breakouts might be an example of your system.
Now here's the trick: we will make this known-profitable system into the add-on trade, the second entry, the "adding to a winning position" trade.
How? By also entering sooner, in the same direction.
For example your known-profitable system might enter long on a 150-day breakout. Great, that's the add-on trade, the second entry. What's the first entry? How about (enter long at (the 150-day breakout, minus (K * ATR))) ? Plug in a value of K that you are comfortable with, such as "enter K=2 ATR's before the 150-day breakout", and ba-da-bing, you're done.
The add-on trade is, by definition, profitable (since it is your known-profitable long term system). The add-on trade benefits you the trader. Whenever the add-on trade is entered, we know for certain that the original entry is in a winning position, in fact we know that it has (profit = K*ATR) when the add-on trade is entered. Voila. We have accomplished the goal of adding onto a winning position, and making the add-ons profitable.
I will let you explore the idea of entering the first position K*ATR before the breakout, and the add-on position N*ATR after the breakout. (Previously we had assumed that N=0. Not any more!). Perhaps it is better, more profitable, higher Sharpe etc, when (K=0 and N>0). Perhaps it is better when (K>0 and N=0). Perhaps (K>0 and N>0) are best. Experiment and find out.