Start-ups raising $100 million or more from investors used to be a rarity. Now, this scale of fund raising is commonplace. In late April, when Mike Massaro set out to get $40 million to $75 million in funding for his payments start-up, Flywire, he contacted a small group of investors he already knew. But word quickly got around, and other investors flooded his inbox with $200 million of investment offers, half of which he turned down.