In a multiuser underlay uplink network, we show that despite the fact that the transmit powers are constrained by the interference temperature limit (ITL) imposed by the primary network, allowing upto two users to concurrently transmit using non-orthogonal multiple access (NOMA) principles ensures better performance than when only a single user is picked in an orthogonal multiple access (OMA) scheme. To deal with the large variation in the link SNRs in underlay networks, an optimal channel state information (CSI) based ITL apportioning scheme is suggested for the first time in literature that carefully controls the transmit powers of the selected users to maximize throughput. CSI-based throughput-optimal strategies are evolved for user selection and NOMA/OMA switching. We analyze the throughput performance of the uplink with NOMA/OMA switching, optimal user selection, and CSI based ITL apportioning, taking successive interference cancellation (SIC) errors into account. Useful bounds on performance are also derived. It is shown that when the ITL is broadcast in every coherence interval, and the ITL can also be channel dependent, large thoughput gains accrue. Computer simulations confirm accuracy of the derived expressions.