Playing in matchpoint pairs of a variable standard, I pick up the following collection as South, dealer at Game all:  

Naturally, playing a weak No-trump, I open 1NT. West Passes mournfully but the opening bid seems to cause partner some sort of a problem. After a long time he emerges with a Stayman 2. This causes no problem to East (who Passes) nor to me - I respond with a dutiful
2. Partner again looks agitated and goes into the office for a little think. Eventually he emerges with 4NT. What now?