Warp drive and the Constellation
My theory, which I'll call WDE ("Warp Drive Evolution") is based on a logical progression of warp speed through increasingly sophisticated technology. Different spacefaring civilizations may arrive at these technological milestones in different ways, but just as TNG and VOY pointed to "transwarp" or "quantum slipstream" as the ultimate means of transgalactic (or, presumably, inter-galactic) travel, so the evolution of any warp technology would be much like scaling a ladder. Each rung is a new milestone in speed and technical achievment. ENT's notion of a "warp five engine" falls in line with this.
In Star Trek, faster-than-light speeds have been expressed in terms of "warp factors". During TOS, Scotty repeatedly made it clear that the NCC-1701 Enterprise could travel as fast as Warp 8 for brief periods with risk. The ship cruised best at Warp 6 or less. Over a century later, Picard's NCC-1701-D Enterprise and Janeway's Voyager seemed to cover more territory at the same or lower warp factors. In TMP3, Capt. Stiles bragged that the Excelsior was going to "break the Enterprise's speed records". Since the experimental TransWarp drive was never used, a conventional warp system would have to be capable of that.
I also noticed that in TOS "Elaan of Troyius" Spock noted of the Klingon vessel "their speed is better than Warp 6." The fundamental visual difference between the warp engines used by Federation starships and those used by the Klingons seemed to be their shape. The eventual appearance of the Constellation-class Stargazer seemed to open the door to a technological answer.
Note the four engines used by the Constellation-class of starships. Note the new shape and bifurcated nature of the Excelsior's nacelles. Here lies the answer: After the NCC-1017 Constellation was destroyed in 2267, Starfleet lent its name to a new concept: what would eventually become the Constellation-class. Rather than the traditional two "circumfirential" tubular warp nacelles, these new ships would use four engines to create a warp-within-a-warp effect.
In the "Introduction to Navigation: Star Fleet Command", pages 5 and 6, a basis is given for how warp drive and warp speed/warp factors work. To quote from "1.2 Warp Drive" on page 5:
"Basically, warp drive consists of the generation of a field about a spacecraft which bends or warps space in the direction of travel. A reaction to the bending propels the ship forward. Since space is being moved relative to itself in a smoothly increasing rate as the center of the field is approached, no neighboring regions exceed the speed of light. However, the total effect on the ship of these incremental speed differences is multi-light velcoities." [NOTE: this falls in line with NASA expert Jesco von Putkammer's remarks in Gene Roddenberry & Susan Sackett's "The Making of Star Trek: The Motion Picture".]
The new concept used in four-nacelle prototypes (which became the Constellation-class) was called LINEAR warp drive. Whereas the most recent subclasses of the Constitution-class could redline at Warp 8 and even briefly acheive double-digit warp factors, these linear-warp driven ships achieved much greater multi-light velocities at lower warp factors. The two converging warp fields accentuated the velocity effect, creating FOURTH POWER warp speeds. The earliest Constellation-class prototypes could only achive Warp 6, but Linear Warp 6 would be faster than Circumfirential Warp 10.9. This technology fell in line with what the Klingons had already been doing for years; thier S-2 Graph Units, which integrated a TWO sets of warp coils into each rectangular unit, were capable of Linear Warp 4, which translated into Circumfirential Warp 6.349: "better than Warp 6".
By the time the Constitution-class was due for a major design overhaul in the late 2270's, Starfleet had followed the Klingon design more closely, integrating both sets of coils into a single, more rectangular Linear Warp Drive housing. [NOTE: during TMP1, the newly refit Enterprise is never said to exceed Warp 7. If Linear Warp 7 is the ship's new top speed, this would roughly equate to Circumfirential Warp 13.39. Also note that in TMP2, Kirk orders Sulu to take the ship to Warp 5 when first headed for Regula; this could be the ship's new cruising speed, roughly equal to Circumfirential Warp 8.55.] If the new NX-2000 Excelsior could achieve Linear Warp 8, this would be equal to Circumfirential Warp 16, which would give Capt. Stiles' remarks to Scotty some weight.
The evolution of linear warp technology continued throughout the rest of the 23rd and 24th centuries, even while the original four-nacelle Constellation-class vessels soldiered on with their unorthodox design. Later encounters with the Romulans and Dominion reaffirmed the viability of this technology. It wasn't until the Borg surfaced as a threat that a major spacefaring power was seen with something advanced beyond linear (fourth-power) warp drive.
The notion of quantum slipstream, aka transcendent warp drive (transwarp), used by the Borg and Voth, introduced the notion of fifth-power warp speeds. Each layer of warp adds disproportionately greater complexity to the drive system because the converging fields must be balanced correctly. (This is why the matter-antimatter intermix malfunction resulted in TMP's wormhole.)