I am aware of Saint Francis of Asisi, but he seems an exception. Under normal circumstances, can a friar (namely, of the Dominican Order) request to be made a deacon but not a priest? Would the request have to be especially justified?
Yes. There are a number of permanent deacons who belong to various religious Orders.
One of my friends is one, and he’s a Benedictine.
The friar, a brother, would need to get permission from his superior.
I suppose some religious orders may choose not to have deacons (and/or priests) as part of their ministry. If that’s the case, the brother would have to leave the community, to start training for Ordination.