Template:Blockquote/styles.css

/* Hanging indent for multi-line attribution */
.templatequotecite .templatequote-cite {
    display: block;      /* make it a block so padding/indent apply to all lines */
    margin: 0;
    padding-left: 2.3em; /* base indent for every line */
    text-indent: -2.3em; /* pull first line back so the dash hangs in the margin */
}

/* Keep the overall visual indent consistent with your existing breakpoint */
@media (min-width: 500px) {
    .templatequotecite {
        /* you already have this; shown here to clarify the math */
        padding-left: 1.6em;
    }
    .templatequotecite .templatequote-cite {
        /* 1.6em (container) + 0.7em (child) = 2.3em total indent */
        padding-left: .7em;
        text-indent: -.7em;
    }
}