After I paid for my policy the company said that upon inspection there was an increase in the replacement cost estimate and I needed to pay an additional $700. Can they do this?
It's an underwriting requirement that you insure your house to its replacement value.
If you don't comply, you can be cancelled or non-renewed.
How much of an increase in Coverage A (dwelling) has been required? From what to what?
$700 seems like a lot of premium increase for an increase in value.
You can check the replacement cost of your dwelling at:
http://www.building-cost.net/Valuation/Start
See if it comes close to what your insurance company is estimating.