As a volunteer at a nonprofit I drove their vehicle for hurricane relief. Can I deduct those miles driven or just the miles put on my own car getting to their warehouse?

I drove all over the state of Florida, plus some in GA and AL from Oct-Dec delivering hurricane relief and transporting animals for a nonprofit 501(c)3 that I volunteered with.  I know I can deduct the miles that I put on my own vehicle driving from my house to the warehouse and back for each trip.  I was told that I could also deduct all the miles that I drove in the company vehicle doing this, is that a correct statement?