Parallel to the development of increasingly mechanistic system-scale modeling approaches in molecular biology, there is a growing interest in attaining a more mechanistic perspective on the evolution of molecular systems. In recent years, several evolutionary simulation approaches and artificial life platforms have been developed to study the evolution of systems. However, modelling the genotype-phenotype relationships of biological systems to a degree of realism that is sufficient for studying the detailed molecular mechanisms of system evolution remains a challenge. We developed a novel genotype-phenotype mapping (GPM) framework to model the expression phenotypes of transcriptional systems from artificial genome sequences, inspired on statistical thermodynamics approaches used to model transcriptional regulation processes. We used this GPM model to study the capacity of several classes of gene regulatory networks (GRNs) to evolve novel phenotypes. We found that the evolvability of identically wired networks with qualitatively the same phenotype strongly depends on the exact genomic sequence of the system under study. Moreover, the evolvability of GRNs towards pre-specified target expression phenotypes is often surprisingly limited, and in most cases crucially hinges on the occurrence of neutral substitutions, with very few direct adaptive paths leading to higher fitness. We also tested whether genome duplication enhances the evolvability of GRNs, and found that, although genome duplication often does increase system evolvability, this is generally far less evident than previously assumed. In brief, the evolution of systems appears to be vastly more complex than anticipated on the basis of the highly abstracted evolutionary simulation models in current use, and we believe that fine-grained modelling approaches such as the one used here will become indispensable to shed more light on the mechanisms and constraints underlying system evolution.