Signal transduction networks can form highly interconnected systems within cells due to crosstalk between constituent pathways. To better understand the evolutionary design principles underlying such networks, we study the evolution of crosstalk for two parallel signaling pathways that arise via gene duplication. We use a sequence-based evolutionary algorithm and evolve the network based on two physically motivated fitness functions related to information transmission. We find that one fitness function leads to a high degree of crosstalk while the other leads to pathway specificity. Our results offer insights on the relationship between network architecture and information transmission for noisy biomolecular networks.