Heat 1 tbsp olive oil in a large skillet over medium-high heat. Add the ground beef and cook until browned, breaking it apart as it cooks—this takes about 5 minutes. Season with 1/2 tsp smoked paprika and 1/2 tsp ground cumin. Transfer to a small bowl and set aside.
In the same skillet, add the remaining 1 tbsp olive oil and the shredded chicken. Warm it through for about 3 minutes, stirring occasionally, then season with the remaining smoked paprika and cumin. Move it to another small bowl and keep warm.
Heat the black beans in a small saucepan over low heat for about 4 minutes, stirring gently so they don't break down too much. Transfer to a serving bowl once they're warm and slightly thickened (yes, they'll look a little watery at first but that's normal).
Arrange your tortilla chips on a large baking sheet or serving platter—don't overcrowd them or they'll get soggy when you add cheese. Spread them out in a single layer and don't worry if there are some gaps. This is the foundation of your loaded nachos entertaining spread.
Mix both cheeses together in a bowl, then sprinkle them evenly over the tortilla chips. Slide the whole sheet into a 375°F oven for about 3 minutes—just long enough for the cheese to get melty and bubbly. Keep a close eye on it after minute 2 so the chips don't burn.
While the cheese's melting, arrange all your toppings in separate small bowls: beef, chicken, black beans, tomatoes, red onion, black olives, cilantro, jalapeños, guacamole, and sour cream mixed with lime juice. This setup makes your party nachos totally interactive and lets everyone customize their plate.
Remove the sheet from the oven when the cheese is melted and gooey. Drizzle the sour cream mixture over top and let everyone add their favorite toppings from the bar. Serve immediately while everything's still warm—this is when loaded nachos entertaining really shines.