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Radio spectrum license is multi-dimensional in nature. This suggests that matching a bid to buy and an offer to sell has to be done across the multiple dimensions to maximize spectrum usage in terms of economic efficiency. In addition, creating a functioning secondary market for trading spectrum requires an intermediary for both pooling the resources and matching the supply and demand sides of the equation. This paper proposes a multiple-dimension auctioning mechanism through a broker to facilitate an efficient secondary spectrum market. A broker for orchestrating the market is proposed describing its basic functionalities. Two trading negotiation protocols, i.e., merchant and auction, are discussed. Focusing on the auction mode, the multiple-winner determination problem (mWDP) is defined and cast into a multidimensional multiple-choice knapsack problem (MMKP). Since the MMKP is NP-complete, two heuristic algorithms to solve the mWDP namely (1) area-by-area (ABA), and (2) maximum-utility-first (MUFA) are presented. Numerical studies illustrating the potential of the algorithms are presented. The numerical studies indicate that MUFA is better in addressing the exposure problem.