That's so nice :)
You could make an offering for your own intentions (without necessarily specifying what they are), I sometimes hear this ("for the intentions of N." or "of the family N.") or, perhaps, "in thanksgiving to saint N." (for being your Patron Saint and interceding for you).
Holy Mass is truly Christ's sacrifice, the same that took place on Calvary, which, having stepped out of time, is now in eternity and shall be repeated every day from east to west, until the end of time.
The benefits that derive from Holy Mass are literally infinite. That is why we often make a pious offering asking the priest to offer the Sacrifice for the sake of departed souls or of the souls of living in need of great help.
To a faithful who asked S. Padre Pio about how great were the benefits of even just attending Mass, he replied: "they cannot be enumerated, you will only be made aware of them in Heaven." And to a saint (who had done great things and received countless blessings from Christ, but I don't remember her name) who asked the Lord in a mystic vision how could she give Him thanks for a lifetime of blessings, the Lord replied: "attend one Mass."
I did not feel this back when I was a candidate myself, but now I love RCIA candidates and catechumens so much that I can hardly express it. :hug1: