Boil the potatoes in a large pot of cold water until fork-tender, about 10 minutes, then drain and cool.

Cook the bacon in a skillet over medium heat until crispy, about 10-15 minutes, and then chop.

In a mixing bowl, combine mayonnaise, Caesar dressing, Parmesan cheese, vinegar, Worcestershire sauce, and celery salt to create dressing.

Add chopped celery and red onions to the dressing along with the bacon, stirring gently.

Incorporate cooled potatoes and chopped hard-boiled eggs into the mixture, tossing carefully.

Cover and refrigerate for at least 4 hours to allow flavors to meld.

Garnish with chopped chives before serving.