Multiparty Session Types (MPST) are a typing discipline ensuring that a message-passing process implements
a given multiparty session protocol, without errors. In this paper, we propose a new, generalised MPST theory.
Our contribution is fourfold. (1) We demonstrate that a revision of the theoretical foundations of MPST is
necessary: classic MPST have a limited subject reduction property, with inherent restrictions that are easily
overlooked, and in previous work have led to flawed type safety proofs; our new theory removes such
restrictions and fixes such flaws. (2) We contribute a new MPST theory that is less complicated, and yet more
general, than the classic one: it does not require global multiparty session types nor binary session type duality
— instead, it is grounded on general behavioural type-level properties, and proves type safety of many more
protocols and processes. (3) We produce a detailed analysis of type-level properties, showing how, in our new
theory, they allow to ensure decidability of type checking, and statically guarantee that processes enjoy, e.g.,
deadlock-freedom and liveness at run-time. (4) We show how our new theory can integrate type and model
checking: type-level properties can be expressed in modal μ-calculus, and verified with well-established tools.