I believe that the number of items you can carry/check is related to the number of passengers, not the number of seats purchased. If you purchased tickets for your whole family and the rest of your family was unable to fly, I do not think you get to utilize their bag quotas.

For example, a parent with a lap baby gets an extra carry-on ("diaper") bag, even though they only purchased one seat. In the example above, you could theoretically turn a flight into a cargo flight: buy a bunch of $19 fares, add a checked bag to each one and lug all the 40 pound boxes you want (99 pounds if you pay an additional fee). There are some limited exemptions for musical instruments and large items, maybe you need to explore that avenue.