  In a previous work [J. Math. Phys. 52, 123504 (2011)], refined algebraic
quantisation (RAQ) within a family of classically equivalent constrained
Hamiltonian systems that are related to each other by rescaling one
momentum-type constraint was investigated. In the present work, the first steps
to generalise this analysis to cases where more constraints occur are
developed. The system under consideration contains two momentum-type
constraints, originally abelian, where rescalings of these constraints by a
non-vanishing function of the coordinates are allowed. These rescalings induce
structure functions at the level of the gauge algebra. Providing a specific
parametrised family of real-valued scaling functions, the implementation of the
corresponding rescaled quantum momentum-type constraints is performed using RAQ
when the gauge algebra: (i) remains abelian and (ii) undergoes into an algebra
of a nonunimodular group with nonconstant gauge invariant structure functions.
Case (ii) becomes the first example known to the author where an open algebra
is handled in refined algebraic quantisation. Challenging issues that arise in
the presence of non-gauge invariant structure functions are also addressed.
