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The possibility for market participants to simultaneously place their bids in different markets across an interconnection is investigated in this paper. Transaction schedulers settle multilateral transactions among participants, while a central entity coordinates the overall operation through interactions with the transaction schedulers. Two issues are dealt with in this context. First, the market participants are allowed to place their bids simultaneously in more than one transactions scheduler's market, and, second, the available transmission capacity is fairly shared among the transaction schedulers. Economically interesting transactions are favored, while confidentiality of market data and independence of transaction schedulers' clearing mechanisms are preserved. The corresponding iterative algorithm is illustrated in detail on a 15-bus as well as the IEEE-RTS system.