I would like to change the membership type
Yes you can change the membership type by visiting the contact and editing membership under membership tab. If the membership amount you want to change to has higher amount than you can ask the member to do balance payment or take offline payment and update the contribution to correct amount associated with membership.

You may need to take care if the user has purchased a membership that will auto renew automatically, if so than you will also need to update the amount at the payment processor gateway so that next time during renewal it charges the correct amount.