I checked my Flavor Bible by Karen Page to see what she says basil goes with. You probably know about this cooking reference, but for those who don't, it's an extensive listing of what flavor goes with what other flavors.
Here's what it says about basil. I boldfaced the ones that are pertinent to the flavor combos of basil with the ingredients in Caesar dressing (parmesan, mostly). I was surprised to see such an extensive listing:
snip
BASIL
(See also Basil, Thai, and Lemon Basil)
Season: summer
Taste: sweet
Weight: light, soft-leaved
Volume: mildmoderate
Tips: Add just before serving. Use to add a note of freshness to a dish.
apricots
Asian cuisine
beans: green, white
bell peppers, esp. red, roasted
berries
blueberries
breads
broccoli
Cambodian cuisine
capers
carrots
CHEESE: feta, goat, MOZZARELLA, PARMESAN, PECORINO, RICOTTA
chicken
chile peppers
chives
chocolate, white
cilantro
cinnamon
coconut milk
corn
crab
cream and ice cream
cucumber
custards
duck
eggplant
EGGS AND EGG DISHES (e.g., omelets)
fennel
fish, esp. grilled or poached
French cuisine
*GARLIC
ginger, fresh
honey
ITALIAN CUISINE
lamb
lemon, juice
lemon verbena
lime, juice
liver
marjoram
meats
Mediterranean cuisine
mint
mussels
mustard: powder, seeds
nectarines
OLIVE OIL
olives
onions
orange
oregano
Parmesan cheese
parsley, flat-leaf
PASTA DISHES AND SAUCES
peaches
peas
pepper: black, white
PESTO (key ingredient)
pineapple
pine nuts
pizza
pork
potatoes
poultry
rabbit
raspberries
rice
rosemary
salads and salad dressings
salmon
salt: kosher, sea
sauces
scallops
sea bass
shellfish
shrimp
soups, esp. Asian, bean, chowder, vegetable
soy sauce
spinach
squash, summer
summer vegetables
Thai cuisine (e.g., green curries)
thyme
*TOMATOES and tomato sauces
tuna
vanilla
veal
vegetables, esp. summer
Vietnamese cuisine
vinaigrettes
vinegar: balsamic, sherry
watermelon
ZUCCHINI
AVOID
tarragon
Flavor Affinities
basil + coconut + curry
basil + garlic + olive oil + salt
basil + garlic + olive oil + Parmesan cheese + pine nuts
basil + hamachi tuna + tomatoes + watermelon
basil + lemon + vanilla
basil + mozzarella cheese + tomatoes
basil + olive oil + Parmesan cheese
snip
The RG can taste in his head. I don't have that gift, so that's why I'm a recipe cook and also why if I have any question when I make up a recipe on my own, I will ask him. If he's not around, I do an internet search to see if others have combined the flavors.
Or, of course, check The Flavor Bible.