There was an option to get the computer with a larger SSD installed when new.
The higher capacity option was 512GB Flash memory SSD, equipped by Apple.
You may be able to inquire & get one of these larger 512GB from an Apple
authorized service provider, or see if OWC finally has an upgrade option.
While there may be a method to repair or replace the SSD, it may or may not
require a qualified authorized Apple trained service technical expert to upgrade.
However there is an iFixit repair guide with sections of replacement instructions:
https://www.ifixit.com/Device/MacBook_Air_13%22_Early_2014
You could contact a vendor such as OWC macsales to see what kinds of modular
flash memory upgrade or replacement units may be available for your MB/Air.
•MacBook Air (13-inch, Early 2014)
Introduced April 2014
Discontinued March 2015
Model Identifier MacBookAir6,2
Model Number A1466
EMC 2632
Order Number MD760LL/B (128 GB storage), MD761LL/B (256 GB storage)
{as indicated from http://mactracker.ca database application archive}
At this point and from the perspective of a user, such as you or me, further info
would be required (perhaps from third party source? such as OWC macsales)
to see if an upgrade option exists, and also inquire (another source such as
iFixit.com repair guides, &/or OWC guides) of any process known to allow or
perform such an upgrade by use of information, that an end user or trained
Apple service provider, to be able to upgrade your model build series MB/Air.
You could use an external Thunderbolt drive enclosure with another SSD inside
for expanded storage and retrieval purposes, or perhaps a rotational 7200-RPM
drive in such a faster data rate enclosure. Such options exist at macsales.com
or other quality Mac-centric venders of longstanding reputation in the community.
As these ASC discussions are essentially user-to-user interaction and do not
necessarily represent any capacity as Apple representatives; though there are
community hosts & people who are here, they don't reply in most threads...
In any event...
Good luck & happy computing! 🙂