Neat interchange I ran into in DC had a traffic circle connecting two avenues with the main avenue diving underneath (since I was driving a truck I had to use the traffic circle to get through as the underpass was 12' 6". ) The were off/ on ramps from the circle going to/from the Avenue to the Circle (controlled by lights where they met the circle. The circle of course had a nice fountain in the middle and what not.
Something remotely like this
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That would be a nice way to connect two avenues with less space than a cloverleaf and less congestion than an at grade intersection.
Also vis a vis Tarkus' idea may be something similar could be done with the outer one ways bedoming the off ramps leading to the circle.
More generally regarding his idea, even if you couldn't change the side by side one lanes appearances just having good working intersections for an 8 lane "avenue" (two one lane roads going in each direction or an avenue flanked by one ways) would work. I have seen major roads where there are separate groups of parallel lanes going the same direction (US 1 coming south off the Tollway in North Philly).