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Constructing heterostructures of a topological insulator (TI) with an undoped magnetic insulator (MI) is a clean and versatile approach to break the time-reversible symmetry in the TI surface states. Despite a lot of efforts, the strength of interfacial magnetic proximity effect (MPE) is still too weak to achieve the quantum anomalous Hall effect and many other topological quantum phenomena. Recently, a new approach based on intercalation of atomic layers of MI, referred to as magnetic extension, was proposed to realize strong MPE [2D Mater. 4, 025082(2017)]. Motivated by this proposal, here, we study a magnetic extension system prepared by molecular beam epitaxy growth of MnSe thin films on topological insulator (Bi,Sb)2Te3. Direct evidence is obtained for intercalation of MnSe atomic layer into a few quintuple layers of (Bi,Sb)2Te3, forming either a double magnetic septuple layer (SL) or an isolated single SL at the interface, where one SL denotes a van der Waals building block consisting of B-A-B-Mn-B-A-B (A=Bi1-xSbx, B= Te1-ySey). The two types of interfaces (namely TI/mono-SL and TI/bi-SL) have different MPE, which is manifested as distinctively different transport behaviors. Specifically, the mono-SL induces a spinflip transition with a sharp change at small magnetic field in the anomalous Hall effect of TI layers, while the bi-SL induces a spin-flop transition with a slow change at large field. Our work demonstrates a useful platform to realize the full potential of the magnetic extension approach for pursuing novel topological physics and related device applications.