Here are some examples of major-type bitonal melodic phrases. They should be drilled in every key around the Circle. You should also be making up your own phrases and drilling them in every key.

Here's a phrase for Cmaj9(#11). The bitonal triad is Bmi. This phrase adds a 4th to the Bm triad. Drill this in every key around the circle. The next chord would be Fmaj9(#11) - the bitonal triad is Emi. The next chord would be Bbmaj9(#11) - the bitonal triad would Ami - and so on.

Here's the phrase through the first 4 keys of the Circle.

Remember this phrase from the Target Notes page? It was given in the context of a Dmi7 chord and I said I basically thought of it as a D Minor Pentatonic with a bunch of passing tones thrown in. We are going to drill the exact same phrase - only now it will be in the context of Ebmaj9(#11). Spelled bitonally that's Dmi/Eb. The scale degree numbers under the notes are the notes relative to the two tonalities. The upper numbers are relative to D minor - the bitonal triad. The lower numbers are relative to the lower, parent tonality, Ebmaj7. Play this phrase in every key around the Circle. Cmaj9(#11) = Bmi/C. Fmaj9(#11) = Emi/F. Bbmaj9(#11) = Ami/Bb, and per the example below, Ebmaj9(#11) = Dmi/Eb.

Here's the phrase in the first 4 keys of the Circle.

Next, the chord is C6/9(#11) - the bitonal spelling is D/C.
This phrase adds a 4th to the D major triad:

In the clip below, this phrase is played through the first 4 keys of the Circle. Notice that in the first key, this D major phrase is played relative to the 6th string C root. The next chord G/F, is played relative to the 5th string F root. Then C/Bb is played relative to the 6th string Bb root, and then the F/Eb is played relative to the 5th string Eb root. This is an example of how drilling something in every position on the neck can provide multiple options directly under your fingertips. I chose positions that resulted in the most economical movement. Less movement = less potential for error.

The following phrase has so many notes added to the D triad that it could be defined in terms of a D Mixolydian mode. However, the first 3 notes of the phrase spell a straight D major triad. In terms of the D major, the whole phrase has an added 6th (B), 7th(C), and 4th(G). The F natural in the 2nd bar is a passing tone between the 2nd(E) and the major 3rd of the D triad(F#). Notice that all the added notes are consonant with the C major parent.

Here is the above phrase in the first 4 keys of the Circle:

These are just a few examples of melodic phrases that can be created over Cmaj9(#11) and C6/9(#11). You should make up many more of your own. They should more-or-less be based on triad and 7th arpeggios. You can then take these melodic fragments and apply them to many different situations as your chordal knowledge allows. As demonstrated above, the same phrase can be used in different contexts. That makes it a different phrase. It's different in terms of the theory - how it relates mathematically to the tonal center - it's different in terms of the way it sounds because of the conceptual difference, but it's exactly the same thing mechanically. That's a beautiful thing because it's the mechanics that take all the sweat and repetition. This approach maximizes the use of every thing you know mechanically. The Dmi phrase above was a Dmi phrase when applied to a Dmi7 chord. But when applied to an Ebmaj9(#11) it became something completely different conceptually, and completely different sound-wise. It is no longer a Dmi phrase, it's now also an Ebmaj9(#11) phrase. You don't have to learn a completely different phrase for every chord. You learn to apply each phrase you know to every chord. Think about a very basic D Minor Pentatonic Blues lick. You can play that exact same lick that you know backwards and forwards without even thinking about it to Ebmaj9(#11) because Ebmaj9(#11) = Dmi/Eb. But you can do this only if you have the knowledge to deconstruct the Ebmaj9(#11) into it's triadic components in order to apply your Blues vocabulary to more complex chordal environments. That's why chordal knowledge is so essential to this approach.