A "qualifying offer" is the market's way of determining which free agents should carry draft pick compensation. The amount for this year is $17.4 million, I believe. If a team extends this to a free agent, and he declines, the team gets draft pick compensation.
My understanding is that the team gets an earlier compensating draft pick if the player signs for more than, rather than less than, $50 million. If a team was willing to make a one year offer of $17.4 million, perhaps that team might be willing to make an offer of that amount for three years, which would take the contract over $50 million. Assuming that the team isn't worried about "decline" issues (say for a player in the late 20s or early 30s), would it make sense for a team to follow up with a three year offer to induce other teams to meet the $50 million threshold? The kind of person I was thinking of was Alex Cobb, of the Tampa Bay Rays, a small market (and budget) team?