Since I don’t know what your “recommended” number was it’s impossible for me to know what a double addition is in this case. Therefore, you should definitely exercise caution before drinking and if your addition was greater than 50 ppm, I would send a sample out for a lab to check it. The legal limit for Free SO2 on wines in the US is 350 mg/L so if it’s over this level, the government would say a wine is unsaleable.
But what if your levels aren’t nearly that high and you want a ballpark answer about the drinkability of the wine? It’s really a matter of your own taste balanced against the level of the addition you made. If you were doing your monthly SO2 addition with topping, and the wine already had SO2 in it, you were probably trying to add around 10–20 ppm total SO2. If you were to add double that amount, it’s not the end of the world.
If you added twice the SO2 (say, you added 40 ppm total), you probably are OK to drink the wine if you give the wine a little time to absorb that level of SO2. SO2 binds up with sugars, aldehydes and other compounds and I find the “dirtier” (more cloudy, unsettled and turbid) the wine, often the more of the SO2 will bind up and go to Total SO2. The Free SO2 is what you would smell or taste. If your wine is young (especially if it was a highly-colored varietal), chances are good that it will “bounce back” from such a big addition quickly, and would be drinkable within a week or two. If your wine was very clean or almost bottle-ready, that much Free SO2 will generally take longer to bind up so I would give it more time before taking a sip, maybe three or four weeks before checking in.