I've contacted the consulate of Greece regarding this question. The response from the Greek consulate was:
Consulate General of Greece in New York
11:28 am (1 day ago)
I understand the problem now. You should contact the Consulate that issued the visa. He might have a problem if he continuously stays in Schengen.
Sincerely,
Consulate General of Greece
ME
Sent: Τρίτη, 4 Φεβρουαρίου 2014 1:30 μμ
To: Consulate General of Greece in New York
Subject: RE: Visa Question
I apologize may be I didn't make it clear the question is actually whether he can remain continuously in Schengen area.
On Feb 4, 2014 12:54 PM, "Consulate General of Greece in New York" wrote:
If the visa is valid then he can use it. You should contact the Consulate that issued the visa as well.
Sincerely,
Consulate General of Greece
Sent: Δευτέρα, 3 Φεβρουαρίου 2014 10:03 μμ
To: grgencon.ny@mfa.gr
Subject: Visa Question
I have a friend who has 2 short term visas granted to me which turned out to be consecutive single entry visas.
Namely, One visa ends on May 2nd and the other begins on May 3rd. How he managed to achieve this I am not sure.
He has a question on whether or not he can continuously remain in Schengen area and what he will need to do to update the information?
He is arriving to Germany on April 19th for the first time in years.
My guess based on the comments received from German and Greek consulates is that consecutive visas is a rarity or should not be issued at all.
Given that I am responding after your intended visit days you might want to add what you have actually done.