Mayonnaise normally already has mustard in it. But yes, you can always add more to improve the taste.

Easy homemade mayo recipe which will taste 1000% better than storebought:

  To a tall container, add in this order:

  Ingredients:
  1 (egg)
  1 soup spoon Dijon mustard (the strong kind)
  1 soup spoon apple cider vinegar
  salt/pepper
  vegetable oil (about 2-3 cups)

  Recipe:
  - Blend ingredients by starting from the bottom and moving your soup blender up and down. Stop blending when it's nice and thick, don't over-blend. Should take 10 seconds or so.