Power systems worldwide are increasingly experiencing the simultaneous failure of multiple components due to severe weather conditions, which are becoming more frequent and intense. This consequently triggers growing interest in more stringent security standards. Indeed, electricity markets are moving toward explicitly including generator outages within auction models seeking the most economical and reliable generation scheduling and dispatch. Within this context, a corrective N-k security-constrained unit commitment model is proposed to address the need for tighter security standards. As a major distinctive feature, the proposed model jointly considers multiple out-of-service generators and lines, corrective actions, and transmission line losses. Moreover, unlike previous studies, lossy shift factors are used to represent the effect of the lossy transmission network while accurately characterizing transmission line losses by a binary-variable-based piecewise linear approximation. Additionally, line outages are incorporated by modeling fictitious injections of active power. The proposed model using lossy shift factors and fictitious injections is cast as an instance of mixed-integer linear programming. The solution of the resulting mathematical problem allows co-optimizing energy and reserves to accommodate the power fluctuations due to the component outages under consideration. Numerical experience is reported using three standard benchmarks comprising 14, 118, and 500 buses.