Magnetotransport measurements in large diameter multiwall carbon nanotubes (20–40 nm) demonstrate the competition of a magnetic-field dependent bandstructure and Altshuler–Aronov–Spivak oscillations. By means of an efficient capacitive coupling to a backgate electrode, the magnetoconductance oscillations are explored as a function of Fermi level shift. Changing the magnetic field orientation with respect to the tube axis and by ensemble averaging, allows the contributions of different Aharonov–Bohm phases to be identified. The results are in qualitative agreement with numerical calculations of the band structure and the conductance.