I have been riding in Specialized shoes for few years and my fitter also recommended arch support. But easiest way to achieve that is through a footbed. Specialized make 3 versions based on the amount of support you need: Body Geometry SL Footbeds | Specialized.com
You just swap out the insole in your current shoe for the footbed. These made a big difference for me - stopped getting numb toes straight away.
p.s. I have the max support (green) footbeds. If you find a Spesh dealer shop they probably have these in store you can try. It will feel really weird to start off, but now I don’t feel them at all.