An LDA (Localizer Directional Aid) approach, a LOC (Localizer only) approach, a VOR DME or ILS DME approach (which may be considered the same as a VOR or ILS by a DE), and a Localizer Back Course approach.
That's all I can think of. My plane had the same equipment for my checkride - DE had me do an ILS, VOR (partial panel) and LDA approach. No problem.
One other thing - if you have DME, expect to do a DME arc.