1) ST:III, which features an Excelsior class with a transwarp drive which is never seen again.

2) TNG, "Where no one has gone before" - an incredulous Geordi reports that "we are passing Warp 10".

3) TNG, "Descent", which features a Borg transwarp conduit. The E-D takes a trip through one of these and covers 60 light years in 8 seconds - an average speed of 236,682,000c.

4) Voyagers "Threshold", which features Tom Paris making a transwarp flight at Warp 10. This episode confirms that Warp 10 is infinite speed.

5) Voyager, "Scorpion", in which 7 of 9 stated that waiting until Voyager crossed Borg space (later found to be about 10,000 light years across) before getting some technology off them would take too long - at the Descent speed, the trip would last less than half an hour!

6) Voyagers Voth species, which featured a transwarp equipped ship. The speed is uncertain, but it seemed to cross about 1,000 light years in a couple of days - an average speed of about 180,000c.

7) TNG's "All Good Things", which features Federation starships in the 2390's capable of routinely going at "Warp 13".

First, I decided that Warp 10 was indeed infinite speed - there was plenty of canon evidence of that. The usual explanation of Warp 10+ speeds is to say that Starfleet recalibrated the Warp scale (again) as ships got faster, to avoid strings of nines ("They're going at Warp 9.999992? Well, take us to Warp 9.99999205!"). However, I've come to dislike this idea. "Where No One Has Gone Before" clearly establishes that you can go past Warp 10 on the TNG era scale. And even though it's been established that Warp 10 is infinite speed, nobody has ever tried to say that Warp 11 is faster still.

So I decided that beyond Warp 10 was a transwarp "domain", and that this established a repeating pattern - a Warp barrier every 10 Warp factors, with 'normal' Warp speeds in between. Warp 10 - 20 was the first domain, Warp 20 - 30 the second, etc. Each domain would be significantly faster than the one below.

So, why bother going at the finite speed of Warp 13 if you can go just as fast by going at Warp 9.998? Well, I decided that it's more efficient. By my calculations, a Galaxy class starship travelling at Warp 9.998 would take about 10¹⁷ Watts, so I adjusted the power curve so that Warp 13 takes about 10¹³ Watts - about what a GCS would takes to do Warp 9.8.

So, to explain the above points one at a time :

1) The Excelsior was designed to go at speeds around the low end of the first transwarp domain - Warp 12 or so. That would be about 47,474c, about Warp 36.2 on the TOS scale.

2) Geordi was amazed that the E-D was able to 'jump' the warp 10 barrier and enter the transwarp realm, something that has been regarded as impossible since the failure of the Excelsior around 80 years earlier.

3) The Borg transwarp conduit is a tough one. Here's what I think happened : The Borg assimilated a new technology just prior to "I, Borg". This allowed them to build ships far faster than their normal ones. They built a prototype ship and sent it out to test it. It was this ship that dispatched the scout which crashed, and from which the E-D recovered Hugh the Borg. When Hugh was returned, the collective on the new ship was destroyed and it drifted until Lore came along. When the collective was destroyed the Borg assumed that the prototype was a failure and gave up on it - it may have taken them huge resources to build the ship in the first place, and with war with 8472 looming they may not have been able to try again.

I don't know if this is true, but it fits every canon fact I can think of.

4) Paris's flight was actually at Warp 10, something no other transwarp drive has done. I had to think up some reasons why it can't be used again - it's a purely one off gimmick, and by my invented 85% fatality rate Paris and Janeway where lucky to survive at all - the chances of at least one of them dying one those flights was over 99.6%, and if Voyager made a single flight home you could expect 127 of the 150 crew to be killed in that single flight. Reason enough not to use it!

5) Standard Borg transwarp is much slower than the experimental ship used in "Descent", so no problems there.

6) Voth transwarp works out to about warp 16.3, in the first transwarp domain.

7) Warp 13 works out to 67,156 x c. That's a big advance on the normal warp drive, but still keeps the galaxy a moderately big place - around 1.25 years to go from one end to the other.
 

All in all, I think this idea makes a lot of sense. It fits every canon fact I can think of, and really it's just an extension of known warp technology. Now if I could just sell the idea to Paramount...