peteharvey

Yes, Infiniti does have a long wheelbase variation of the midsize Q70, called the Q70L with a wheelbase that's 6 inches longer, and overall length that's more than 7 inches longer, teamed with a 5.6L V8 - this is sort of a "de facto" full size sedan.

Wheelbase
2,900 mm (114.2") Q70; 50 mm (2") longer than GS.
3,051 mm (120.1") Q70L; 200 mm (8") longer than GS!

Length
4,945 mm (194.7") Q70
5,131 mm (202.0") Q70L

Width 1,845 mm (72.6")
Height 1,509 mm (59.4")

When North America's Infiniti general manager was interviewed, he said something along the lines that a genuine full size sedan would do great for Infiniti's image, but such a car wouldn't be very profitable.
That's probably why Infiniti uses a "de facto" full sized stretched wheelbase Q70L 5.6 V8 on the same platform and same sheet metal as the midsized Q70, rather than build a true dedicated full size luxury V8 powered saloon.

Below, spot the difference in the rear doors & rear windows; Infiniti Q70 5.6 V8 versus Infiniti Q70L 3.7L V6.
Note how having the de facto full sized stretched wheelbase Q70L available with the smaller 3.7L V6 engine further adds to the confusion.

In reality, I guess it's not just size that distinguishes a midsize from a full size, but also the styling, so that the flagship is perceived as a totally different car from the ground up to justify its quality and price, rather than just a stretched wheelbase alone which should only add a few thousand dollars to the price tag.

Contrary to rumours of an impending full sized "Q80", personally I believe such a full sized Infiniti should be designated "Q90", for a trio of odd first digits: Q50 compact, Q70 midsize, and Q90 full size.