As a foil to Modern's high contrast and sensuous curves, why not look as faces with even type color and clean lines?

I tended to use News Gothic with the old Moderns.
I got the idea from Raymond Lee, my mentor, so I felt that I was party to an authentic tradition.

Not being a typographer, my first guess would have been to use Bodoni Book with Modern No. 20.

But that would not look good - they aren't the same typeface, and so if one uses two different typefaces, one wants contrast.

So, I would then consider the suggestion that a real typographer made above, News Gothic. But when I look at it, I think that it's not quite right.

Times Roman? No. Almost as bad as Bodoni Book.

A slab serif, like Memphis or Cairo or Stymie? That seems to me to be what would work, supplying what News Gothic lacks (serifs, so important for the readability of body copy) and yet contrasting strongly with Modern No. 20 in about the same way that News Gothic would. (Being short and squat instead of tall and thin, the contrast is doubled. This may be a bad thing, though, and if so it explains the choice of News Gothic.)

As an alternate suggestion, one could try Optima, but I think that would be pretty iffy as well.

Ray never used Modern 20, though.
He preferred Bodoni with News Gothic.
The trick was to match the weight of the serifs to the weight of the sans.
And throw in a few similar line rules as well.

I'd be tempted to look at Helvetica Neue, Avant Guarde for a nice round contrast or Dinn for something a little different.