We do not have any extra room in our vehicles to transport extra luggage to Gotenba Station prior to the climb.
You can mail your bags to your next destination or return with us to Tokyo where you can store your luggage in coin lockers at Shinjuku Station.
Mailing your bags by 'takkyubin' (postal service) to your next destination is surprisingly cheap at about US$20 for next day shipping for any check-in sized bag. You can mail your luggage from your hotel counter (most common) or from any Seven Eleven convenience store in Japan! Here is a webpage with more information.