No. You may if you like, and it may be salutary for you, but it should by no means be considered recommended. I think you’re overwhelming yourself by trying to say as many prayers as you can. I’d, however, recommend something very different: stop saying prayers, and start praying.
Mental prayer and meditation are not often stressed enough in our prayer lives. If we pray nothing else, a 15-minute meditation on some perfection of God or incident in the life of Christ every morning is most necessary. The Rosary, indeed, is a blend of vocal and meditative prayer, but its great worth is not so much through its collection of Aves and Paters but through its call to contemplate the mysteries of the lives of Christ and Mary. Many a time while praying the Rosary, I’ve lost the words mid-Ave while my conscious thought was drawn to some aspect of the mystery on which I was meditating.
So, Saphire, instead of worrying about what vocal prayers you should add to your devotional regimen, you’d do best to take some time in silence, preferably at the start of the day, simply letting your heart ponder upon the mysteries of God and of His kingdom. Let that move you to greater piety and love for God, and let it be the wellspring from which your Rosaries and all your other vocal prayers flow.
For more clarity on this, I’d definitely bring this matter to your parish priest or some other trusted priest or religious, who knows your soul far better than any person here.