  We study the implications of a combined analysis of cosmic standard candles
and standard rulers on the viability of cosmological models beyond the
cosmological concordance model. To this end, we employ well-established data in
the form of the joint light-curve analysis supernova compilation, baryon
acoustic oscillations, and cosmic microwave background data on the one hand,
and a recently proposed set of quasars as objects of known brightness on the
other hand. The advantage of including the latter is that they extend the local
distance measures to redshifts which have previously been out of reach and we
investigate how this allows one to test cosmologies beyond $\Lambda$CDM. While
there exist various studies on parametric extensions of $\Lambda$CDM, we
present here a comparative study of both parametric and fundamental extensions
of the standard cosmology. In order to keep the scope of this manuscript
contained, we focus on two particular modifications: One is the consistent
theory of two interacting spin-2 objects, so-called bigravity, and the other
conformal gravity, a theory of gravity that has no knowledge of fundamental
length scales. The former of the two constitutes a veritable extension of
General Relativity, given that it adds to the metric tensor of gravity a second
dynamical tensor field. The resulting dynamics have been proposed as a
self-accelerating cosmology. Conformal gravity on the other hand is a much more
drastic change of the underlying gravitational theory. Its ignorance towards
fundamental length scales offers a completely different approach to the origin
of late time acceleration. In this sense, both models offer - in one way or
another - an explanation for the dark energy problem. We perform a combined
cosmological fit which provides strong constraints on these extensions. We also
briefly comment on the implications of the long-standing $H_0$-tension.
