You can absolutely do that. If you want to upgrade to a paid plan to get some of the features you want, then you can switch at any time through the My Products option in your account or with the help of a GoDaddy Guide. Once you upgrade your site will have all the same customizations and work that you've already put in place, just with the added features. See Website Builder plans and pricing for more info.
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However, there are some big downsides. You aren’t actually able to amend the mobile version of your website when you’re working from a desktop, while SimpleSite’s premium plans are relatively expensive overall compared to other website builders should you want to access more features. While it does have a free plan, the premium options range from $9.99 to $28.95 per month.
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