Apply for Tier 2 while already working in the position

[ismith]

Hello,

I recently finished studying in the UK and am currently on a Tier 4 Doctorate Extension Scheme (DES) visa. On this visa I am allowed to work in a full-time permanent position. I have been offered a permanent position recently with a company that is willing to sponsor me on a Tier 2 visa. However, they may not have a CoS directly available as they are a small company and I am not sure if they updated their yearly allocation this year. If they don't then they would need to request one from the Home Office and that could take up to 18 weeks I have read. I am speaking to their visa person next week, but in the mean time I had a question:

Would it be possible for me to begin working in the permanent position with them while on my DES, and then once the CoS is available, apply to switch to Tier 2 status? My concern is that I will be applying for a Tier 2 visa tied to a position for which I will already be working. If this is possible, what start date would we put on the CoS?

I haven't found any information on this because it's a pretty specific case. My thinking is that it would be OK, as at all times I will be covered by a visa which allows me to work in a permanent position.

If anyone has any thoughts or suggestions, I would really appreciate it!