bland soup

I would say you should reheat and add chicken base that will fortify the bland chicken stock and if needed more salt to taste. You can buy the chicken base in the grocery store it is a paste in a jar an very cheap.

I have the same problem with my kiddos who love bland food - gack! I usually add a whole mess of cholula to my bowl chicken soup along with some cheese on top and pretend I meant to make it that way.

A splash of white vinegar and some fresh cracked pepper.

Fresh herbs, fresh cracked black pepper, fresh cut carrots/celery, caramelized onions. Call me crazy, but chicken soup is one of the few things I like to keep "sweet," meaning, not salty. I like it to taste of chicken essence... it might be the latent jewish grandmother in me...

Probably too late now, but I would probably have stuck it back on the stove in the morning and simmered to reduce it further, and then just added salt. Chicken broth can take lots of add-ins (carrots, celery, etc.) to round out and enhance flavor, but fundamentally requires nothing more than chicken, salt, and maybe some onion for a perfectly robust flavor.

Julienne some fresh carrots and zucchini and cook for a few minutes.

soy, fish sauce, worsterchire, all add salt and fish sauce really is salty but gives a nice flavor. i add it to all kinds of things such as stews, soups, braises. some fresh sautéed celery is flavorful with the right flavor profile.

Ginger for a more Asian-profile.
Smoked paprika
Curry powder
Thai curry paste
scallions
fresh herbs like parsley, thyme, basil

Lemon juice and salt

Salt? MSG? Cognac? Soy sauce? Bacon?

How about some tabasco? You could add a bit of cayenne or regular hot sauce too.