Genetic programming has found recent success as a tool for learning sets of features for regression and classification. Multidimensional genetic programming is a useful variant of genetic programming for this task because it represents candidate solutions as sets of programs. These sets of programs expose additional information that can be exploited for building block identification. In this work, we discuss this architecture and others in terms of their propensity for allowing heuristic search to utilize information during the evolutionary process. We investigate methods for biasing the components of programs that are promoted in order to guide search towards useful and complementary feature spaces. We study two main approaches: 1) the introduction of new objectives and 2) the use of specialized semantic variation operators. We find that a semantic crossover operator based on stagewise regression leads to significant improvements on a set of regression problems. The inclusion of semantic crossover produces state-of-the-art results in a large benchmark study of open-source regression problems in comparison to several state-of-the-art machine learning approaches and other genetic programming frameworks. Finally, we look at the collinearity and complexity of the data representations produced by different methods, in order to assess whether relevant, concise, and independent factors of variation can be produced in application.