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 costs while guaranteeing high availability requirements. The whole assessment is supported by an experiment based on the containerized IMS platform Clearwater which we deploy to derive some realistic system parameters by means of fault injection techniques.