Ceilings of major planes OEI

How high can the major passenger planes fly OEI?

I think Embraer 170 is said to have ceiling of 6100 m OEI. What about the major long-haul twins, like Boeing 767, Boeing 777, Airbus 330? And the Dreamliner?

Trijets and quadjets have better performance OEI than do twinjets, and for that reason, they are allowed to continue to destination OEI. How much better is another matter, since they do not have as much reserve thrust as do twinjets.

What are the OEI ceilings of Boeing 747, Airbus 340 and Airbus 380?

Also, while quite some private planes are widebodies, most are narrowbodies, like ACJ and BBJ. Which are both twins and therefore have serious OEI limitations. What are their ceilings OEI?

There is only one currently successful and in production and development trijet series, namely Falcons. What are the OEI ceilings of Falcon 900? Falcon 7X?

Also, how maneuverable are OEI twinjets at or near their OEI ceiling? Is it a serious problem for them to follow valleys and pick up passes while flying below the summits?