Sensory processing differences, including responses to auditory, visual, and tactile stimuli, are ideal targets for early detection of neurodevelopmental risks, such as autism spectrum disorder. However, most existing studies focus on the audiovisual paradigm and ignore the sense of touch. In this paper, we present a multisensory delivery system that can deliver audio, visual, and tactile stimuli in a controlled manner and capture peripheral physiological, eye gaze, and electroencephalographic response data. The novelty of the system is the ability to provide affective touch. In particular, we have developed a tactile stimulation device that delivers tactile stimuli to infants with precisely controlled brush stroking speed and force on the skin. A usability study of 10 3-20 month-old infants was conducted to investigate the tolerability and feasibility of the system. Results have shown that the system is well tolerated by infants and all the data were collected robustly. This paper paves the way for future studies charting the sensory response trajectories in infancy.