  Mutually unbiased bases (MUBs) provide a standard tool in the verification of
quantum states, especially when harnessing a complete set for optimal quantum
state tomography. In this work, we investigate the detection of entanglement
via inequivalent sets of MUBs, with a particular focus on unextendible MUBs.
These are bases for which an additional unbiased basis cannot be constructed
and, consequently, are unsuitable for quantum state verification. Here, we show
that unextendible MUBs, as well as other inequivalent sets in higher
dimensions, can be more effective in the verification of entanglement.
Furthermore, we provide an efficient and systematic method to search for
inequivalent MUBs and show that such sets occur regularly within the
Heisenberg-Weyl MUBs, as the dimension increases. Our findings are particularly
useful for experimentalists since adding optimal MUBs to an experimental setup
enables a step-by-step approach to detect a larger class of entangled states.
