your first example is wrong. E6 has C#, not C natural. So a C+ can't be derived from E6 since C natural isn't there

the second example is a needlessly complicated way of explaining it.

here's how it works: Use augmented chords like secondary dominants.

---example---

| C | Am | F | G | ---> | C,,, E+ | Am,,, C+ | F,,, D+ | G,,, G+ |

As always, season to taste.