Of course this makes me suspicious
Incidentally, I agree with all the folks that would overcall 1S at the first round.
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What are the suit requirements of double followed by bid of own suit ?
If the requirements are having a decent 6 card suit OR a VERY GOOD (at the very least AKTxx) 5 card suit, then this hand does not comply.
I think that the risks of double + new suit is greater than missing a 5-3 fit in spades (likely if we double again), which might well not exist at all: indeed, if pard is very weak with a singleton or void in spades, he should pass (if we double then bid a suit and he is broke, he will assume our suit is good and pass before it's too late), and that is the last thing I want.
Pard will read my 2nd double as "cards", mostly takeout oriented, and frankly, even in the worse case scenario (we miss 53 fit in spades), our hand offers enough safety in any suit pard can pull to (likely diamonds).

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