If $125M is the top offer, and the player is highly disappointed, then he could try for a 1 year mega deal to try to increase value, but at JD's age, and the fact that it might be hard to top 2017, unless he gets 700 PAs, he'll just have to "suck it up" and settle for a measly $125M.
JD may shed a tear, but I won't.
I wouldn't be surprised, if the Sox have offered $120M/5 with the stipulation that they be given a chance to up another higher offer. $125m/5 might be a safer offer, so as not to antagonize JD or BorA$$, but why go higher right away, when you might be the only guy in town?