  In symmetric teleparallel geometry the curvature and torsion tensors are
assumed to vanish identically, while the dynamics of gravity is encoded by
nonmetricity. Here the spatially homogeneous and isotropic connections that can
accompany flat Friedmann-Lemaitre-Robertson-Walker metric come in three sets.
As the trivial set has received much attention, we focus on the two alternative
sets which introduce an extra degree of freedom into the equations. Working in
the context of symmetric teleparallel scalar-tensor gravity with generic
nonminimal coupling and potential, we show that the extra free function in the
connection can not play the role of dark matter nor dark energy, but it
drastically alters the scalar field behavior. We determine the restrictions on
the model functions which permit the standard cosmological scenario of
successive radiation, dust matter, and scalar potential domination eras to be
stable. However, the alternative connections also introduce a rather general
possibility of the system meeting a singularity in finite time.
