No, Apple does not perform upgrades on this model laptop after purchase. AFAIK there are no third party SSDs for this laptop since this SSD uses yet another different & unique and proprietary Apple SSD connector. While an Apple Authorized Service Provider could technically order & install a larger Apple SSD in the laptop it would be extremely expensive. Regardless most AASPs will not order the drive this way as it goes against the standard Apple parts/repair guidelines (or they don't realize it is "possible" to order a larger SSD). A new Apple laptop would actually be cheaper anyway (yes an Apple SSD is that expensive).
You should check to see if you qualify for this free Apple SSD repair program:
https://support.apple.com/13-inch-macbook-pro-solid-state-drive-service
FYI, here is the current list of publicly acknowledged free repair programs for various Apple products (some such as your laptop have multiple programs):
https://support.apple.com/exchange_repair