Advanced multi-threaded programs apply concurrency concepts in sophisticated ways. For instance, they use fine-grained locking to increase parallelism and change locking orders dynamically when data structures are being reorganized. This paper presents a sound and modular verification methodology that can handle advanced concurrency patterns in multi-threaded, object-based programs. The methodology is based on implicit dynamic frames and uses fractional permissions to support fine-grained locking. It supports concepts such as multi-object monitor invariants, thread-local and shared objects, thread pre- and postconditions, and deadlock prevention with a dynamically changeable locking order. The paper prescribes the generation of verification conditions in first-order logic, well-suited for scrutiny by off-the-shelf SMT solvers. A verifier for the methodology has been implemented for an experimental language, and has been used to verify several challenging examples including hand-over-hand locking for linked lists and a lock re-ordering algorithm.