Panasonic have released firmware v2.2 for the Panasonic GH4 that adds 4:3 anamorphic support at a resolution of 3328 x 2496.
The benefits of this are an increased shallow depth of field, higher resolution and a cool 2.66:1 aspect ratio. This would then need to be cropped slightly if you want a more standard 2.39/2.40:1 ratio.
During recording in the GH4 anamorphic mode the HDMI output cannot be used in 8-bit. In 10-bit mode however, the camera outputs via hdmi at 2880×2160, but internal recording is disabled.
The new firmware can be downloaded here: