We advance a performability assessment of a multi- tenant containerized IP Multimedia Subsystem (cIMS), i.e.: one and the same infrastructure is shared among different providers (or tenants). Specifically, we: i) model each cIMS node (a.k.a. Containerized Network Function - CNF) through the Multi-State System (MSS) formalism to capture the dimensionality of the multi-tenant arrangement, and characterize each tenant through queueing theory attributes to catch latency-dependent performance aspects; ii) afford an availability analysis of cIMS by means of an extended version of the Universal Generating Function (UGF) technique, dubbed Multidimensional UGF (MUGF); iii) solve an optimization problem to retrieve the cIMS deployment minimizing cost...