You can upgrade your subscription by choosing one of the subscription tiers above your current level in the subscription menu. If you choose to upgrade your subscription you will get a price deduction based on the period you have left of your current subscription, which means you will only pay the price difference.
When you upgrade to another subscription tier you're buying a new subscription, which means your subscription starts over from day 1 and not just the time you had left on your previous subscription.
Please note that you'll keep your latest coupon from you previous subscription when you upgrade, but this does not mean you have two subscriptions, only that the last coupon remains until you use it or the validity runs out.