  Very-high-energy (VHE) BL Lac spectra extending above $10 \, \rm TeV$ provide
a unique opportunity for testing physics beyond the standard model of
elementary particle and alternative blazar emission models. We consider the
hadron beam, the photon to axion-like particle (ALP) conversion, and the
Lorentz invariance violation (LIV) scenarios by analyzing their consequences
and induced modifications to BL Lac spectra. In particular, we consider how
different processes can provide similar spectral features (e.g. hard tails) and
we discuss the ways they can be disentangled. We use HEGRA data of a high state
of Markarian 501 and the HESS spectrum of the extreme BL Lac (EHBL) 1ES
0229+200. In addition, we consider two hypothetical EHBLs similar to 1ES
0229+200 located at redshifts $z=0.3$ and $z=0.5$. We observe that both the
hadron beam and the photon-ALP oscillations predict a hard tail extending to
energies larger than those possible in the standard scenario. Photon-ALP
interaction predicts a peak in the spectra of distant BL Lacs at about $20-30
\, \rm TeV$, while LIV produces a strong peak in all BL Lac spectra around
$\sim 100 \, \rm TeV$. The peculiar feature of the photon-ALP conversion model
is the production of oscillations in the spectral energy distribution, so that
its detection/absence can be exploited to distinguish among the considered
models. The above mentioned features coming from the three models may be
detected by the upcoming Cherenkov Telescope Array (CTA). Thus, future
observations of BL Lac spectra could eventually shed light about new physics
and alternative blazar emission models, driving fundamental research towards a
specific direction.

High Energy Astrophysical Phenomena;High Energy Physics - Phenomenology