We do not currently allow participants to create their own cards, although this is intentional.
All participants must sort the same cards in order for your data to remain cohesive and in line with one another.
Additionally, allowing participants to add cards means that they could essentially create a completely new sort for themselves by adding a significantly large number of cards. This would change their sorting patterns and categorisation, making it near impossible to compare their data with the next person.
As a workaround, you can add post-study questionnaires asking participants if they felt like there were missing items, or items they expected to see but didn't. Some researchers will also edit their Instructions to point participants in the direction of the Feedback button in the top right corner of the card sort and add any card labels they feel might be missing from the card options on the left hand panel.