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The scramble I've used has the following phases:

1. Cars and pedestrians can cross one direction

2. Cars and pedestrians can cross other direction

3. Pedestrians can cross any direction

That would be perfect. In Quebec city it is illegal to follow cars in the direction of the green light. If there is a pedestrian signal, you must call for it and wait which makes it awfully long and inconvenient. Takes about 30sec to a min before we can cross most intersection but hey "its safer" they say.

Does that mean cars can never turn at that intersection?

If an intersection is busy enough with pedestrian traffic the left and right turns are impossible without a dedicated turn phase I think the traffic engineers can handle that slight modification. The US has a plethora of lights where turns are made explicit with green/red arrows. As a pedestrian I am not supposed to cross when the turning traffic has a green arrow as the walk sign is always the red hand.

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