Shuttle-based storage and retrieval systems (SBS/RS) store stock keeping units in a multi-tier rack, where autonomous shuttles move them horizontally and one or more lifts vertically. In classical tier-captive designs each shuttle is bound to a single storage tier. Tier-to-tier systems gain flexibility by allowing the shuttles to change levels, so that fewer vehicles than tiers can serve the whole rack. The performance is strongly influenced by the tier-change movements. This paper presents an analytical method to estimate the throughput of a system variant, in which a shuttle-lift transports shuttles across tiers and the I/O area. The results are validated against simulation and examples of model usage are given.