Yes, one standard form is:
"As a [role] I want [requirement] so [value statement] and there can be attached artifacts to explain further." It's a 'place-holder'.
"As a JobSeeker I want to sell myself on criteria other than a list of tech, so that I can project a fuller picture of myself"
Attach text: "e.g. sell myself to a recruiter on the basis of my potential as an employee rather than in a simplistic "what's your experience of X in years or on a scale of 1-10"
or a diagram, though that could come out in the conversation you have with the developer who will write the code, later. There is no intermediary analyst to provide an extra interface for communication to get screwed up and you go into a tight cycle of code & demo to check you've understood, maybe splitting a story or thinking of new ones.
Sometimes user-stories are declared to be 'epics' that can be split into many stories. This might be one, if you can think of independent stories for different types of criteria you want to record.
Developers will also think of tasks that need to be done to make each u-s possible but you only do things just in time and just as much as needed. I know less about this because I wasn't deeply involved with that part of the process.
An important feature of a u-s is it's independence, so that it can be written, declared 'done' and be deliverable, preferably delivered, so the customer can get experience of using the software and give feedback to inform later decisions.