Incorporated in FL but doing business in PA
I presume you are referring to sales tax you would be charging your clients. If you company is incorporated in Florida then any order that you sell in Florida would be taxed at the local rate (meaning state rate if you are shipping to a county other than yours, or state+county rate if you are shipping within your county).
If you are opening a branch in Pennsylvania and will have your company registered in that state as foreign entity then you would need to do the same with Pennsylvania orders, meaning you would add Pennsylvania state sales tax on orders shipped within Pennsylvania but outside the county where you are shipping from, or state+county tax for orders shipped within the county, assuming this county has additional sales tax.
If you are shipping to clients outside Florida and Pennsylvania you don't need to collect sales tax from those orders at all.