Yes, this is possible for monthly Per User licenses. The number licenses can be adjusted monthly up or down. Read here how you can easily adjust the number of licenses in the AppExchange by yourself.
Yearly Per User licenses can be increased throughout the year, for the remaining of the contract period.
To downgrade is possible, but it will take effect only at the start of the new contract period.
The Site license is an organization-wide, yearly license, for an unlimited number of users. There is no need to purchase additional licenses, nor is any extra administrative handling needed.