Don't let Greek take over
I completely agree with some of the concerns raised in this discussion about not allowing all of the Greek language. Allowing modern Greek would likely result in the site eventually being overrun with Greek questions and Latin questions would slowly fall into the background, which is the original focus of the site. The change would effectively turn this site into a Greek Language site which happens to allow Latin questions as well.
Thinking about the impact, in 2012 there was an estimated 13,000,000 speakers of the Greek language, whereas the number of speakers of the Latin language isn't even measurable because it's so small and most scholars who study it do not actually speak it.
Drawing lines is hard
Not allowing modern Greek but still allowing ancient forms of Greek leaves us in an itchy spot. Creating cut-off points doesn't always work. It may sound easy and straight-forward now, but it will only cause confusion and arguments in the future. Not everyone will understand that only some of Greek is allowed if you advertise that they can ask Greek questions. Not everyone will understand the difference between ancient and modern Greek. Not everyone will agree that something belongs in the "category" (for lack of a better term) of modern Greek and not ancient Greek, or vice versa.
If your discussion devolves into drawing an imaginary line that you think will keep the scope focused, then you better be prepared for that line to end up looking like this after a while:
And this is for something meant to be a side-topic, of all things.
Think back to the Area 51 process
You ran a Latin proposal through Area 51, and acquired a mass of users interested in the subject of Latin. Nowhere in there was there any mention of Greek, nor can you assume that any of the users who wanted this proposal to succeed have any interest of abilities in Greek. To throw out some numbers from the Greek proposal currently on Area 51, only 14.1% of those followers had followed the Latin proposal, and there is currently not even a high enough percentage of users active on this site following that proposal to show up in the list.
To me, it looks like Greek is targeting a completely separate audience than that of Latin. Yes, the Greek proposal is approaching its cut-off date of the one year mark, but just because a proposal is about to fail doesn't necessarily mean that we should go and shove it into some other site in hopes that it will survive somewhere it just doesn't belong. Those users are always welcome to try again.
Ultimately, we need to be thinking about what is best for Latin Stack Exchange, and not what might help other proposals. Will including Greek into Latin's scope improve this site? I haven't seen a lot of arguments of how it will, but mostly arguments of "well, why not?" I've seen a lot of reasons of how it might damage the site, so maybe it's not such a great idea.
It's unlikely that we will support changing the name and/or URL of the Latin site to include Greek components. However, the decision to allow various, smaller subsets of Greek questions is ultimately up to all of you and your willingness to moderate such content.