pastoral care: parishioners with mental illness

I recently read Howard W. Stone's Depression and Hope: New Insights for Pastoral Counseling -- which I was optimistic about based on the table of contents, etc., but which failed to live up to that optimism.

From page 67:

Obviously some depression is so severe that it requires hospitalization. The vast majority of melancholics seen by ministers and other church professionals are only mildly depressed, however, and will benefit from skillful pastoral care. [...] As a rule of thumb, ministers do best to see mildly and some moderately depressed individuals, referring the more serious cases to pastoral counseling specialists or mental-health professionals. Both minister and congregation, however, still offer support and pastoral visitation to seriously depressed members who are on medications, have periodic psychotherapy, or are in and out of psychiatric hospitals throughout their lifetimes.

The author doesn't really elaborate on what this "support" would look like, and I am genuinely curious -- you who are in pastoral ministry or pursuing that vocation -- What do you do if you have a parishioner who struggles with severe depression that includes suicidal ideation and self-harm impulses? This hypothetical parishioner has a qualified psychotherapist they see weekly, is on psychiatric medication that seems to be working fairly well, and is "high-functioning" enough to hold down a steady job and present as "fine." But this person was also suicidal enough to go in-patient at a psychiatric hospital for a few days recently. As their pastor, what do you see as your role in their support system? (They have explicitly stated that one thing they need is more one-on-one time with you. How frequent do you imagine that one-on-one time to be? What do you imagine those pastoral care sessions might entail? What do you do if you have a lot of other time commitments -- e.g., a second job, a family, commitments to other justice organizations -- where do you place these pastoral care sessions in your prioritizing of your time?)

I would be hard-pressed to "define" pastoral care (though I'm developing ideas), and I am really interested in what actual pastors would say in answer to this question. (And also what parishioners might want pastors to say.)