  In the newly discovered magnetic topological insulator MnBi$_2$Te$_4$, both
axion insulator state and quantized anomalous Hall effect (QAHE) have been
observed by tuning the magnetic structure. The related
(MnBi$_2$Te$_4$)$_m$(Bi$_2$Te$_3$)$_n$ heterostructures with increased tuning
knobs, are predicted to be a more versatile platform for exotic topological
states. Here, we report angle-resolved photoemission spectroscopy (ARPES)
studies on a series of the heterostructures (MnBi$_2$Te$_4$, MnBi$_4$Te$_7$ and
MnBi$_6$Te$_{10}$). A universal gapless Dirac cone is observed at the
MnBi$_2$Te$_4$ terminated (0001) surfaces in all systems. This is in sharp
contrast to the expected gap from the original antiferromagnetic ground state,
indicating an altered magnetic structure near the surface, possibly due to the
surface termination. In the meantime, the electron band dispersion of the
surface states, presumably dominated by the top surface, is found to be
sensitive to different stackings of the underlying MnBi$_2$Te$_4$ and
Bi$_2$Te$_3$ layers. Our results suggest the high tunability of both magnetic
and electronic structures of the topological surface states in
(MnBi$_2$Te$_4$)$_m$(Bi$_2$Te$_3$)$_n$ heterostructures, which is essential in
realizing various novel topological states.
