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Striker Jay May is on the verge of moving to Bromley from north Kent rivals Dartford.
May, who is out of contract, is expected to sign at the weekend with his fee being fixed by an independent tribunal.
Bromley manager Mark Goldberg, who is overhauling his squad, said: "We have agreed everything with Jay and as far as I'm concerned he will be playing for us next season.
"Because he is under 24 and we cannot agree a fee with his club, it will go to a tribunal."
May follows striker Warren McBean into Hayes Lane after he moved from Sutton earlier in the week. His fee will also be fixed by a tribunal.
Goldberg has also swooped for Eastleigh central defender Karl Murray who comes in as a straight replacement for former Player-of-the-Year Tutu Henriques who left the club earlier this month to play in South Africa.
The Bromley boss is also in the market for a left-back and plans to have talks with an unnamed player over the weekend.