In stacks of two-dimensional crystals, mismatch of their lattice constants and misalignment of crystallographic axes lead to formation of moir{e} patterns. We show that moir{e} superlattice effects persist in twisted bilayer graphene with large twists and short moir{e} periods. Using angle-resolved photoemission, we observe changes in valence band topology across large parts of the Brillouin zone, including vicinity of the saddle point at M and across over 3 eV from the Dirac points. We also detect signatures of potential secondary Dirac points in the reconstructed dispersions. For twists $theta>21.8^{circ}$, scattering of electrons in one graphene layer on the potential of the other leads to intervalley coupling and minigaps at energies above the gap due to cone anti-crossing, usually considered the only low-energy feature due to interlayer coupling. Our work demonstrates robustness of mechanisms which enable engineering of electronic dispersions of stacks of two-dimensional crystals by tuning the interface twist angles.