What to feed my senior cat

My cat is 16 years-old. He recently had been throwing up a lot. He was throwing up both dry and wet.  It turns out that he is allergic to the food I have been feeding him for the past 16 years. The vet said to go with a grain-free food, which I did. He went to Wellness and loved it....for about a week, then stopped eating it. I then went to Blue Buffalo Wilderness. He loved the Salmon flavor for about 9 days. He ate everything on his plate with both Wellness and Blue Buffalo, then I began throwing out can after can. He kept going for his dry. I keep dry down for him all the time, because it won't spoil like canned can during the day. My sister who lives with me has begun eating meat again (I am a vegetarian) and gave him bits of sliced turkey and Bumble Bee Prime Fillet Solid White Albacore. Now he won't eat any canned at all. He begs at the fridge now. Last night I cooked him some chicken and he ate that. I know that cats need cat food and not human food.  There is nothing medically wrong with him. What can I give him to get him back to canned food? 

Thanks...

What symptoms was he showing in terms of allergies? I find it a bit odd that he ate that food for 16 years and was fine, then suddenly not fine. However, grain free is a better way to go with cat food. Many, many people have fussy cats who will eat a food with gusto one day and refuse the next (my cat does this too). It's extremely frustrating. I'm just wondering if you could keep on feeding him his kibble supplemented with cooked chicken and tuna. Personally, at his age I wouldn't want to get into long drawn out battles to get him eating his food.

Thanks for the reply. I plan on having my cat be the first to reach 100 years old...lol.  His symptoms were vomiting as soon as he ate it, no matter what the flavor and after every meal, or almost every meal.  Constantly coughing, but nothing coming up. At first we though it was asthma, but the vet ran a test and said not likely. Then we fed him some of his regular food, and within 5-8 minutes he started vomiting and coughing. She said she believes it is an allergy. Because he ate it for so long, I guess it is common for cats to develop allergies after being on the same thing for a very extended time. When I put him on the grain-free, the vomiting and coughing were gone and surprisingly immediately. But, now he won't eat it. I think he got used to my sister feeding him the fresh meat. I like your idea though. Keep him on the dry and feed him real meat on the side. Just worried about him, and throwing out $4-$6 worth of food a day is really adding up.  If he hadn't just had a workup, I would think it was something else. But, besides him not eating the can, nothing else has changed. He still follows me around, wants to be with me constantly, uses the litter box regularly, unless I have clothes on the floor, dirty or clean, makes no difference to him (lol...but he has done that since...well for as long as I can remember). He sleeps with me every night, visits our guinea pigs, loves to be held and plays a lot.  I was worried because he all of a sudden started drinking more water than usual, so I called his vet and she said it is the dry food, but if it is in extreme amounts give her a call back immediately. I am monitoring his water intake very closely right now. Thank you for your reply.