Make existing cheesecake recipe chocolate?

I have a cheesecake recipe that I have used many times, and absolutely love. I also love chocolate. So I was thinking, why not combine the two? There are plenty of recipes out there for chocolate cheesecake. My concern is that these are all new and different recipes to me, and while there is nothing wrong with that, I was wondering if I might be able to simply use the recipe I already know?

My thinking was that I would melt some semi-sweet chocolate and mix it into the batter, perhaps with a dash of chocolate extract as well to enhance the chocolate flavor. Is this a reasonable approach? or would the addition of the melted chocolate change the consistency/character of the batter such that it wouldn’t work, perhaps not setting up properly or something? Would there be any caveats I should be aware of, or adjustments I would need to make for it to work?

Apparently (according to comments) the specific recipe makes a difference, and the technique can’t be generalized to cheesecakes in general, or baking in general. As such, here is the recipe I use. Nothing special, it’s just one I know works and produces results I like. It actually came from the box of cream cheese originally:

1 cup graham cracker crumbs
3 Tbsp. sugar
3 Tbsp. butter, melted
5 pkg. (8 oz. each) PHILADELPHIA Cream Cheese, softened
1 cup sugar
3 Tbsp. flour
1 Tbsp. vanilla
1 cup BREAKSTONE’S or KNUDSEN Sour Cream
4 eggs

Heat oven to 325°F
Mix crumbs, 3 Tbsp. sugar and butter; press onto bottom of 9-inch springform pan. Bake 10 min.
Beat cream cheese, 1 cup sugar, flour and vanilla with mixer until well blended. Add sour cream; mix well. Add eggs, 1 at a time, mixing on low speed after each just until blended. Pour over crust.
Bake 1 hour 10 min. or until center is almost set. Run knife around rim of pan to loosen cake; cool before removing rim. Refrigerate 4 hours.