Increase the quantities of everything equally for more servings - the method is the same, it will just take a little longer to bring the soup to a simmer. This soup is best served freshly made so I recommend just making what you will need at the time.
Pimienton dulce, sweet smoked paprika, is more typical but you could use picante (spicy) if you prefer.
Some versions add some Spanish serrano ham into the soup, crisping it slightly with the bread or as a garnish so feel free to add some. As mentioned above, another variation adds the egg more as egg drop - if you prefer this, gently beat the eggs before adding. Stir the soup so it is moving a bit then add the egg and continue to stir so it cooks and separates at the same time. If you choose this method, you will probably need less eggs (even half) but you can judge to taste.