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.