Either in conjunction with, or shortly after, you should secure a second contract with a national carrier. The biggest myth in ecommerce operations is the idea that the best shipping rates are found with a single carrier. In fact, carrier sales reps will go so far as to sell you on that specific point, and "customize" the contract to make you feel like the rate is as optimized for you as possible. Then they throw in volume breaks so that if you hit a certain limit, you get even bigger discounts.
Meanwhile, the reason the carrier sales rep needs your estimated shipping volumes is because they put the volume breaks near that threshold. Their job is to get as close to 100% of your volume as possible.
We have talked to countless companies who insist their rate with a specific carrier is the best possible in the world so it makes zero sense to add a second. They couldn't be more wrong.
In truth, carrier contracts are set up so that a customer "saves" money with some combination of properties, but the carrier "makes" the money back with other properties. For example, maybe it's a great rate for packages under 1 pound but a terrible rate over.
The condition people tend to under appreciate is the variability of orders and shipping, combined with the weekly volatility of rates and surcharges, combined with the hidden constraints of a carrier's network. It's almost always the case that engaging with two or more carriers using multiple methods allows for the business to arbitrage rates, SLAs, and reliability against each other to gain greater cost savings, faster speeds, more reliable delivery, and happier customers.
We typically see a business with two carriers pick USPS as one of the carriers and UPS, FedEx, or DHL as the other. This is because USPS is uniquely specialized at smaller parcel sizes, so many companies opt to prioritize USPS for small domestic shipments then fall back to another carrier for larger or international shipments.