One thing I forgot to suggest above is Andrographis, a herbal tonic, which is said to help stimulate the immune system.
The person I share house with has used it several times when she has felt the early symptoms of a cold of flu coming on. She said the symptoms after that were much milder and the cold was shorter in duration. I know this doesn’t qualify as empirical evidence, but it’s here for what it’s worth.
Anyone considering trying it should check on it’s possible collateral effects first.
Bugs Bunny: "I speak softly, but I carry a big stick."
Yosemite Sam: "Oh yeah? Well I speak LOUD! and I carry a BIGGER stick! and I use it, too!" BAM!