The fabrication of MnBi2Te4 family of materials has been demonstrated that intercalating magnetic MnTe layer into topological insulator Bi2Te3 is an efficient way to explore magnetic topological insulator. A natural question is that if multiple MnTe layers can be intercalated into Bi2Te3, meanwhile if the topological properties are well preserved. Based on first-principles calculations, we first confirm that multiple MnTe layers can be inserted into Bi2Te3 by forming antiferromagnetic MnnBi2Te3+n (n = 1–5) crystals, where each system is energetically stable and can be readily exfoliated down to a monolayer. Specifically, the structural phase transition from ABC to ABAC stacking happens when n ≥ 2. Further electronic band structure calculations and topological identification reveal that the magnetic MnnBi2Te3+n undergoes a topologically nontrivial to trivial phase transition when n > 2, which is attributed to that multiple MnTe layers destroy the topological property of Bi2Te3. In addition to applying compressed strain, the topological states can be restored by intercalating Bi2Te3 layers by forming (MnTe)n(Bi2Te3)m heterostructures. Most strikingly, it is found that the topological properties of (MnTe)n(Bi2Te3)m are universally determined by the ratio of n/m, once n/m ≤ 2.8, the desired topological states are recovered. Our notable findings enrich the family of magnetic topological insulator, providing opportunities to explore more intriguing topological phenomena.