I’ve gotten a couple of True Brew kits where the yeast "use by date"was expired. I bought a new yeast packet for each kit and just added the one new packet.
Since I am new to brewing (just 6 kits so far) I don’t know what would happen if I used the new yeast and also the old expired yeast with the same batch. Yup, I’d really like to know.
I’m told there are no “dumb” beer questions so I am hoping that this qualifies as a legitimate yeast question.
Dry yeast packets? You can add the old one along with the new. If liquid, I would make a starter and see if you get any activity, might be able to get it going enough to pitch just that one.
Most likely even though it’s past the expiration date, there’s still viable yeast in there, although not as much as fresh. Also depends on how it was kept in the store. High temps would tend to lead to shorter shelf life. If the kits you are getting from a particular store consistently has expired yeast, then their turnover must be low, and ingredient freshness is questionable. Either get fresher ingredients elsewhere, or convince alot of your friends they need to explore a new hobby. 
Sorry about the longwinded answer. To directly answer your Q, if you add an old package and a fresh package of the same yeast strain, no biggie, you’ve just added a little extra yeast. If different yeast strains, one will dominate, but how can you tell which one?
When I started last year, my 1st 3 batches were 'Truebrew’s. They had ‘Munton’ yeast, without any strain designation. After the 1st batch I replaced the yeast with US-05 and saved the Muntons for emergencies( they’re still sitting in my fridge).
[quote=“James Rausch”] If the kits you are getting from a particular store consistently has expired yeast, then their turnover must be low, and ingredient freshness is questionable. [/quote]I agree with this. Dry yeast, if fresh is usually good for a year to a year and a half, US-05 anyway. If the yeast is packed with the kit then there’s a good chance the extract and the specialty grains are that old too.
You can also add the expired pack to the boil for nutrient for the fresh yeast you buy.
