I have multiple allergies and will be attending a company dinner at a restaurant where we have to order from a set (and very limited) menu. I don't see anything on this menu that looks safe at all, and this restaurant serves a kind of food that isn't really friendly to my allergies. Can I discreetly bring in some food of my own to eat?
Many -- but not all -- restauranteurs are sympathetic to your predicament. If a restaurant truly can't accommodate your multiple allergies at a large dinner like this one, many will not mind your discreetly eating an alternate meal. The same goes for weddings and catered parties.
It's a breach of etiquette, however, to assume that your best option is to bring your own meal and that the restaurant will look kindly on your doing so. The proper course of action is to call the restaurant manager (preferably at a non-peak time, after the lunch rush but before dinner) and explain your situation. She can let you know whether they have some safe options and give you information about cross-contamination. You may be pleasantly surprised -- some restaurants really do "get it." You can also ask about bringing your own food and having some wine, salad, or plain side dishes at the restaurant -- whatever you and the restaurant agree is likely to be safe.
What if you're assured that the restaurant can accommodate your allergies but you get answers about issues like cross-contamination that concern you? In this case it's essential that you don't eat anything that might cause a reaction. Explain your situation to human resources and see about staying for the cocktail hour or eating on your own beforehand and coming late. You'll get many of the social and career benefits of the company dinner without the health risks.
There is one exception to the general rule about bringing food into a restaurant without asking -- few restaurants will bat an eye about small quantities of snack food brought for a preschool-age or younger child. While this obviously doesn't apply to most company dinners, it's a good rule of thumb to keep in mind.