Full lightfield AR displays would have no issue with this. Even some hypothetical giga-sandwich of waveguide planes like a Magic Leap 1 on steroids could do an effective approximation of this.
(Assuming by "mix depth to objects with the real world" you mean "having virtual objects alongside real objects with convincing depth alignment")
(Assuming by "mix depth to objects with the real world" you mean "having virtual objects alongside real objects with convincing depth alignment")