Can I thin thick PVC cement with primer?
I use MEK (methyl ethyl ketone) available at most hardware stores. It has always worked for me and I've never had a fitting failure yet. I have had fittings fail from using thickened glue. Granted it's not the best thing to do, and I always buy a new can as soon as possible. But I do know where you're coming from when you need to do something to be able to finish a job, and can't run to a store at 3 am, or when you are 30 or more miles from any supplies. 

Being that is the main ingredient in most welding adhesives or glues. Look at any MSDS Sheet and you will see the solvent used in it. For example: 
http://www.speedlinepvc.com/user/pdfs/5152-pdfs-5-file.pdf

I know I'm satisfied with my results. 
And storing that can upside-down always helps. I've even spread a bit of the glue around the top of the can to dry into a seal if I know I'm not going to use it for a really long time.