Let \(\Omega \subseteq \mathbb{R}^N\) be a bounded domain with a \(C^2\)-boundary \(\partial \Omega\). The authors consider a parametric Dirichlet problem of the form \[ \begin{cases} -\operatorname{div}a(z,\nabla u(z))=\lambda (\xi(z) u(z)^{-\eta(z)} +u(z)^{\tau(z)-1})+f(z,u(z)) \quad\mbox{in } \Omega,\\ u \Big|_{\partial \Omega} =0, \, \lambda>0, \, u > 0, \, \eta, \tau \in C(\bar{\Omega}), \end{cases} \] with \(0<\eta(z)<1\) for all \(z \in \bar{\Omega}\) and \(\max_{\bar{\Omega}} \tau < \min_{\bar{\Omega}} q\) for a suitable \(q\in C(\bar{\Omega})\) involved in the working hypotheses. The principal map \(a(z,\cdot): \mathbb{R}^N \to \mathbb{R}^N\) is continuous, strictly monotone (hence maximal monotone too) and has nonstandard growth involving a variable exponent \(p(\cdot)\) in the space of all Lipschitz continuous real functions \(C^{0,1}(\bar{\Omega})\). The right hand side of the equation exhibits the combined effects of three nonlinear terms, namely a singular term \(\xi(z) u^{-\eta(z)}\), a concave term \(u^{\tau(z)-1}\), and a Carathéodory perturbation \(f(z,u)\). The authors establish the existence and multiplicity of positive solutions in Theorem 4.10, that is a bifurcation-type result describing the changes in the solutions' set as the parameter \(\lambda\) varies on the positive real half-line. The approach is mainly based on fixed-point arguments together with the theory of monotone-type operators. Some special cases of map \(a(z,\cdot): \mathbb{R}^N \to \mathbb{R}^N\) are discussed in the last section of the manuscript.