New employer?

[fikys]

Hi,

I'm currently work for an University on the Tier 2 visa which expires in August 2013. I recently passed interview at another University. They say that they have to apply for CoS for me by a certain day within a month (to make sure this is done within 6 months of the advert).

There is a slight chance that I might stay with my old employer but most likely I'll move to the new place.

It seems I might have a period when I'll have CoSs from two different universities at the same time.

Is this a problem for the Immigration office at all or I can just choose one of the CoSs by the time I apply for my new visa (either for new or old university)?

Thanks!