MLBTR has reported these teams are interested in players linked to the Sox:
Burnes: BOS, TOR, SFG
Flaherty: BOS, BAL, NYM
Buehler: BOS, NYM, NYY, CHC, DET, OAK
Castillo (trade) BOS, NYM, BAL, CHC
Cease (trade) BOS & BAL
Bregman: BOS, PHI, TOR, DET (No LAD, NYY or NYM) Maybe we get Alex.
Teoscar: BOS, LAD, TOR (NYM were before Soto signing)
Santander: BOS, NYY, TOR
Arenado approved a trade to 6 teams: BOS, NYM, PHI, SDP, LAD, LAA
Although there was no money bid on Crochet, the NYM and NYY were interested. I realize this is not the same as outbidding for a FA.
Now, if the NYM win on any of these guys, they will likely drop out of the race for some others, so maybe the Sox win one of those bidding contests, although one may not be able to say we "outbid Cohen." I am not sure the Yanks are going to bid heavily on some of those they were linked to, earlier.
It does look like lAD< NYM and NYY will not win every bidding war on all the players listed, above, so I do think we can win one or two of them, if JH refuses to be outbid.