In this paper, we consider a multi-cell multi-user MISO broadcast channel. The system operates according to the opportunistic beamforming framework in a multi-cell environment with variable number of transmit beams (may alternatively be referred as the transmission rank) at each base station. The maximum number of co-scheduled users in a cell is equal to its transmission rank, thus increasing it will have the effect of increasing the multiplexing gain. However, this will simultaneously increase the amount of interference in the network, which will decrease the rate of communication. This paper focuses on optimally setting the transmission rank at each base station such that a set of Quality of Service (QoS) constraints, that will ensure a guaranteed minimum rate per beam at each base station, is not violated. Expressions representing the achievable region of transmission ranks are obtained considering different network settings. The achievable transmission rank region consists of all achievable transmission rank tuples that satisfy the QoS constraints. Numerical results are also presented to provide further insights on the feasibility problem.