Four-Party Line by Dorothy Gilman Butters (1954)
There is FRANCINE, with whom snobbery was a rule until her at-first-sight-love of Tom gave her a compassion for all people; and PEGGY, whose restless ambition brought her marriage to the brink of ruin; and TIPPY, who, in her loneliness, looked with despair even upon her own good disposition; and MARY, who came from the wrong side of the tracks with a secret wish, and attained it.
Although their backgrounds are varied, a common bond results from working side by side in the oft-times dramatic atmosphere of the switchboard room. For one girl somehow touches the life of the next and, in so doing, adds understanding where there was none before.
Here is a new setting for the problems of human relationships, happily resolved in an intriguing way. (from the inside flap)