Tricky Situation with travel to EU/Shengen Visa

Hi I am a British citizen and my wife has an application with the authorities for her British Citizenship, she applied in early Feb and we are still awaiting the result. She is due to fly to Greece with me on 16th of May for a week, we initially thought that we would get the result by mid April, following which we could complete the formalities for British Passport (Optimistic).

She has a valid Schengen visa till 19th May and now i guess the best option is to apply for an extension as she would have to be there till 24th of May.

Current Schengen Visa Valid Till: 18th May
Flying to Greece: 16th May
Flying Back: 24th May

doubt/question:

- Is it possible to apply from Schengen visa (for extended stay) when you already have a valid schengen visa
- If not, what are the options available
- We have already taken appointment for Greece Visa which is on 1st of May, would this be cutting really close,considering it is a holiday period and we fly on 16th.

Thanks

Anyone with any thoughts????

Anyone with some thoughts? Will be appreciated?

You haven't mentioned what nationality your wife holds, but see the guidance below.
"Greece Visa application and processing time
You can apply for a Greek Schengen visa 90 days before your planned trip. Usually the visa application process takes a minimum of 5 working days, therefore you are advised to apply 3 weeks in advance of your planned trip.

For the nationals of the following countries the application time takes at least 14 working days (Source: VFS Global):

Afghanistan, Algeria, Bangladesh, Belarus,D.R. Congo, Egypt, Iran, Iraq, Jordan, North Korea, Lebanon, Libya, Mali, Mauritania, Morocco, Niger, Nigeria, Pakistan, Rwanda, Saudi Arabia, Palestinian travel documents holders, Somalia, South Sudan, Sri Lanka, Sudan, Syria, Tunisia, Uzbekistan, Vietnam, Yemen."