Once or twice I’ve been part of a public praying of the Rosary in which the steady recitation of the Hail Mary is interrupted. This is usually difficult, breaking, as it does, the steady rhythm of a familiar and repeated prayer. I don’t find it works. But maybe you agree with the document:
201. The custom of making an insertion in the recitation of the Hail Mary, which is an ancient one that has not completely disappeared, has often been recommended by the Pastors of the Church since it encourages meditation and the concurrence of mind and lips (Cf. SC 90).
Insertions of this nature would appear particularly suitable for the repetitive and meditative character of the Rosary. It takes the form of a relative clause following the name of Jesus and refers to the mystery being contemplated. The meditation of the Rosary can be helped by the choice of a short clause of a Scriptural and Liturgical nature, fixed for every decade.
The Directory on Popular Piety and the Liturgy is online at the Vatican site.