The PS4, when placed in a horizontal position, should have a sufficently large flat surface on the top of the unit. This allows easy stacking of the PS3 on top of the PS4 in order to provide excellent and 100% compatible backwards compatibility to all current PS3 owners.
Put a small divider between the two, get some quality tape, tape them together. Get a decent Plastic casing, preferably custom molded. Encase the PS4 and PS3 in it. Engrave PS3+4 or something cooler on the custom casing. You're all set!!!
That's it. I will build a PS7 before Sony even gets the idea for it!
Most men want to open doors for themselves.
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On the subject of PS4/BC, unfotunately I don't think this would be a solution - the PS3 (all models) is not flat on top and another system would just slide off. The PS2 would work better for BC, since both models of PS2 were flat .