Anisotropic plasmonic nanorods offer a wide range of applications in photovoltaics, energy conversion, sensing, and surface-enhanced Raman spectroscopies. However, achieving control over the size and shape of the surface overcoating on these nanorods remains a challenge due to the complexity arising from the multistep wet chemical processes involved in their experimental synthesis. Here, we show that by employing data imputation and data augmentation methods, we can minimize the limitations of a small experimental data set and successfully train supervised machine learning models that can optimize the experimental synthesis. Using a small data set collected from 30 multistep syntheses of silica-overcoated gold nanorods (GNRs) characterized by optical extinction spectroscopy and transmission electron microscopy, we trained complementary supervised models to predict the overcoating shape of the nanorods using optical spectral features. The effects of experimental parameters and measurements made during different stages of the synthesis were analyzed. Our approach enabled us to design an experimental synthesis recipe to yield a target SiO2 overcoating shape on GNRs employing inverse design optimization. The developed workflow can be extended to other plasmonic nanoparticles and multistage synthesis experiments, where a limited data set is available to understand the effects of synthesis parameters and to establish correlations between measurements and synthetic yields.