It's always best practice to remove old solder and start fresh, especially on small components that are difficult to visually inspect.
You want it to be as close to eutectic as possible to have a reliable temperature profile and minimize imperfections. Mixing alloys creates unpredictable results.
The graph shows the relationship of temperature and phase for Pb/Sn alloys. Lead-free would obviously have a different graph for each alloy, but they're specific and scarce.
Any significant change to the alloy and you will likely increase your liqidus plastic temp and duration range, thereby increasing the odds of dull joints and microfractures.
It probably will still work as long as everything is stationary and evenly heated/cooled. But given how easy it is to wick first and how much of a pain it is to reball a bga, I don't take the risk.