I have a Schengen visa issued by Greece, which will expire in December of this year.
Can I apply for a new one now, even while my visa is still valid? I just want to anticipate the timing. Do I apply with the same requirements?
Yes, it's possible as long as the visa dates don't overlap. E.g. if your visa is valid until December 31st, you should apply for a new visa starting on January 1st. The Handbook for the processing of visa applications and the modification of issued visas mentions:
Example: A Moroccan lawyer representing a gender equality NGO who frequently participates in meetings in various Member States holds a multiple-entry-visa which expires on 31.5. She applies for a new visa on 15.4.
If a new visa is issued, it should be valid from 1.6. and in such a case the visa holder would be entitled to enter the territory of the Member States on the basis of the first visa that will expire during the stay and leave on the basis of the new visa.
The requirements for applying for a new visa will be the same as for your previous one, although you might qualify for a multi-entry visa depending on your previous travel history.
Yes you can, if your trip starts in three months or less. Assuming you have a multiple-entry visa valid for more than six months, you can even apply up to three months before the expiry date of your current visa (as opposed to three months before your next trip). This stems from article 9 of the Schengen visa code:
Applications shall be lodged no more than three months before the start of the intended visit. Holders of a multiple-entry visa may lodge the application before the expiry of the visa valid for a period of at least six months.