Yes.  you may change subscription plans at anytime.  Your existing account will continue work as it is in the new subscription plan.  However, a paid plan cannot be downgraded to the free basic plan.  

If you are on a monthly subscription and upgrade to a higher plan within 10 days of the last monthly payment, we will automatically refund the previously made monthly payment in that month. Credit Cards are processed through PayPal, but a PayPal account is not required. Click on 'Pay using your credit or debit card' on the PayPal login page after clicking on 'Subscribe' button in CaseFox."