In this work, we explore methods to improve galaxy redshift predictions by combining different ground truths. Traditional machine learning models rely on training sets with known spectroscopic redshifts, which are precise but only represent a limited sample of galaxies. To make redshift models more generalizable to the broader galaxy population, we investigate transfer learning and directly combining ground truth redshifts derived from photometry and spectroscopy. We use the COSMOS2020 survey to create a dataset, TransferZ, which includes photometric redshift estimates derived from up to 35 imaging filters using template fitting. This dataset spans a wider range of galaxy types and colors compared to spectroscopic samples, though its redshift estimates are less accurate. We first train a base neural network on TransferZ and then refine it using transfer learning on a dataset of galaxies with more precise spectroscopic redshifts (GalaxiesML). In addition, we train a neural network on a combined dataset of TransferZ and GalaxiesML. Both methods reduce bias by $\sim$ 5x, RMS error by $\sim$ 1.5x, and catastrophic outlier rates by 1.3x on GalaxiesML, compared to a baseline trained only on TransferZ. However, we also find a reduction in performance for RMS and bias when evaluated on TransferZ data. Overall, our results demonstrate these approaches can meet cosmological requirements.