Hi CCoffey,
I’m not sure of the length of the span between the sides of your bed but if it’s not more than the width of a twin mattress (about 38") then you could use 5/8" good one side plywood (preferably low VOC … see here) on top of your bed to provide good support without needing center support. The down side to this would be a lack of airflow under the mattress which in combination with other risk factors could increase the risk of developing mold or mildew in your mattress (see post #10 here) although in most cases it would probably be OK if not ideal. You could also use a bunkie board to provide good support across the two sides your mattress which would be more breathable (see post #4 here and the post it links to) or you could add a bed rug on top of the platform to improve the ventilation under your mattress as well.
Phoenix