x264: suppose I set a bitrate higher than the lossless rate?

[ChiDragon]

What is the resulting video, as compared to the original?

Do I get lossless + overhead? An approximation? Something else entirely I'm not considering?

[Brother John]

Visually lossless? Most likely yes. Bitwise lossless: No because the lossy algorithms throw information away, no matter how high you set the bitrate. In practice your encoded video might not even reach the desired bitrate because the encoder was saturated (i.e. couldn’t make it any larger) earlier.

[Sagittaire]

Visually lossless? Most likely yes. Bitwise lossless: No because the lossy algorithms throw information away, no matter how high you set the bitrate. In practice your encoded video might not even reach the desired bitrate because the encoder was saturated (i.e. couldn’t make it any larger) earlier.

Theoriticaly you can have higher bitrate for lossy codec than lossless codec ...

[Dark Shikari]

You can effectively set a precision higher than lossless by using an absurd CQM (and thus potentially get a higher bitrate). But because of rounding errors in the transforms and so forth, it won't actually be lossless -- just very very close.