It depends what you consider as a "overlap". Ancient Greeks are close but they are distinguishable in every PCA expect for the one Jovialis posted.
0.038 distance is not overlapping in my book, close, but not that close as Ukrainians and Poles are with Pagan Slavs.
In a nutshell, my opinion:
Latins/Etruscans and other Italic people in red. (Even though some genetic variation, IMO did exist in the South so I don't believe all Italic tribes were identical to Latins). The old Greeks in purple circle, in black circle the Imperial Romans and parts of West Asia in yellow circle.
To me it seems that Imperial Romans were created with a varying degree of Middle Eastern and Latin/Central Italic admixture. Those who lean Italic, cluster as Southern Italians and those lean more Anatolian/Levantine are obviously more eastern forming a tail around the modern Aegean Greeks, especially Cyprus towards the Anatolia and Levant.
If you ignore Mycenaeans and hypothetically use Southern Italians as a proxy for say, 90% Greek transplants. You will get a a 80% replacement of Italic people in Abruzzo and 70% replacement in Lazio.