Bi-tonality using the circle of fifths relationship between keys is as good a starting point as any for controlling the level of dissonance I would have thought. Combining triads from keys that are distantly related in the circle will obviously give higher levels of dissonance than those lying closer together. This approach stresses superimposition rather than substitution and is a good way of retaining a connection to the original harmony of a tune if you're reharmonizing.

The other tools you might employ if you're thinking harmonically of non-triadic structures is Paul Hindemith's notion of interval tonics and degree of dissonance of each interval type.

So Maj 2nds, Maj3rds 5ths, maj6ths and maj7ths all have lower note tonics. minor 2nds m3rds 4ths m6ths and m7ths all have upper note tonics. the b5th being ambiguous in this regard.

Using the distance between interval tonics as a guide, you can easily see that chord or line formed by maj3rds built on C and D is less dissonant than one yielded by maj3rds on C and Eb, which in turn is less dissonant than maj3rds starting on C and F# for example.

Things obviously become more complex when you factor in the inherent dissonance level of the intervals you employ. But even here you can see that a chord made up of Major 7ths on C and F is less dissonant than one with Maj7ths on C and Eb.

Hindemith's classification of chords in terms of dissonance level is based on their intervallic makeup with the most dissonant being structures containing the highest number of adjacent minor seconds, more than one flatted fifth and whether or not the resultant chord suggest a tonic.
A useful comparison is Ernst Krenek's classification which i must confess i didn't know of until I read :

consonance and dissonance

Hope this is nearer to what you had in mind.

Alan