Thanks for your enquiry!
Kindly note that the VaR threshold is based on monthly exposure, meaning that not all your positions have a 10% VaR.
The RM takes into account several aspects, including the number of trades you open in a given month, the volatility when you open the trades, etc.
While there are several aspects that could have an impact in your example, if you hold 2 positions and close the EURUSD exposure, the RM would do the same (i.e. close your EURUSD exposure).
If I understood your example correctly, by closing your EURUSD exposure you'd not be increasing your overall's VaR, on the contrary, you'd be reducing your overall exposure (say you had 0.1 EURUSD lots and 0.1 GBPUSD lots, bu closing 0.1 EURUSD lots you'd be reducing your total exposure).
Going back to your question, I don't think the RM would make an additional long trade in an example like yours.
I hope this proves helpful!