1. D major - B7 - E major: This is a classic modulation that uses the dominant seventh chord of E major (B7) as a pivot chord. The B7 chord contains the leading tone (C♯) which resolves to the tonic (E) in the E major chord.
2. D major - G major - C major - E major: This progression uses a series of secondary dominant chords to modulate to E major. The G major chord is the dominant of C major, and the C major chord is the dominant of E major. This creates a smooth and logical progression from D major to E major.
3. D major - Bb major - E major: This progression uses a deceptive cadence in the first chord change. The Bb major chord is the relative major of G minor, which is the relative minor of C major. This creates a harmonic surprise and leads to the final dominant-tonic resolution in E major.
4. D major - Em7 - A7 - D major - E major: This progression uses a chromatic mediant relationship between D major and Em7. The Em7 chord shares two notes (E and B) with Am7, which is the dominant seventh chord of D major. This creates a smooth transition to the A7 chord, which then resolves to D major. The final D major chord acts as a pivot chord, leading to the final resolution in E major.
These are just a few examples of chord progressions that can modulate from D major to E major. Ultimately, the choice of modulation will depend on the overall musical context and the desired effect.