Even Jose will tell you this isn't true.
Modulations can occur in a number of ways, and oftentimes in a very short period of time. Basic diatonic progressions are fairly uninteresting, and, well, basic. I'd like to first talk about cadences, specifically ii chord substitutions as techniques for modulations. Technically ii chord substitutions contain notes that are out of the key; Take for instance, the Italian Augmented Sixth. This chord cannot be "spelled" as a triad, yet it has melodic gravity towards the V. While the flat sixth occurs naturally in a minor key, it is an accidental in a major key. The sharp four does not occur naturally in either. Also in this family are the French and German Augmented Sixth Chords, as well as the Neopolitan Chord. While these aren't modulations, persay, they lay the groundwork for substitution chords which do include modulations.
There can be an argument for a V7/V chord to be a modulation. The dominant chord substitution contains notes that gravitate towards the V of your original key, which would, for a moment, make the the "new key" the V of the original key. However, if you create a dominant chord off of the V chord by adding the minor seventh, you are again modulating back to your original key; the power of the cycle of fifths. Yet, perhaps one could make a progression of V7/V - V7 - I7 - iv. This is a common technique to create a modulation to the key of the iv chord, which would also technically make the progression listed above as VI7 - II7 - V7 - i. All of these chords do not belong to one specific key, and all of these chords can occur in a fairly short period of time, within the same progression (i.e. 4-8 bars).
Furthermore, it is quite common to use the diminished chord as a sort of "passing" chord that functions in a similar fashion as a passing tone functions within a melody. Diminished is almost the garbage dump of melodic harmony; when all else fails, a diminished chord will likely work. Using a diminished chord as a pivot point in a progression to establish a new key is quite common (e.g. Gmin - G#dim - Amin). Again, not too drawn out, and can be accomplished within the same chord progression.
Half-step motion into a modulation is yet another technique which can be used. Oftentimes, jazz players will call this "playing modally." I'm going to use a specific example for the illustration of this concept: Mediterranean Sundance - Al Di Meola. The progression for the solo section is mostly in E minor/G major, however closer to the end the chord progression goes into a bit of A min (E phrygian). The progression is as follows: Emin - Amin - D7 - Gmaj - F#maj - Fmaj - Emin - D7 (there's a bit more to the end, but it's completely irrelevant to what I'm talking about). Notice that, up until the F#maj, all of the chords occur diatonically within the aforementioned key(s). However, after that, Di Meola uses a half-step motion to accentuate the change into E phrygian by way of the Fmaj, which then continues until the D7, which pivots him back into a G major feel until the deceptive cadence contained within the end of the progression which propels him back into E minor, all within the same chord progression.
tl;dr: It is definitely possible to have multiple modulations within the same chord progression.
In terms of progress...I've got nothing thus far. my next 2 weeks are completely booked, finals week and then i'm going to New York the whole of the following week. I should start composing in about 3 weeks hopefully. Dave, I hope you make the deadline to be somewhere near the end of April!
