What's to stop players from making fighters, with maxed out engines, that then have another stage above that.

Wasted mass.

If you put two sets of engines on a ship, and only one set is running, then the ship will be slower not faster in either mode of operation than if it had only that set of engines.  If both sets can be used simultaneously, then again its top speed will be slower than if you had dedicated the same amount of mass to using "fast" engines.  And if you make the fuel consumption of engines vary non-linearly with power output, you're changing fuel consumption/endurance, not speed.  In other words, I don't recall seeing anyone proposing a different power/weight ratio for engines in this thread; it's just a proposal for making endurance longer when a ship is "cruising" (slowly) between stations.

John

It's certainly possible, it is just rarely done.  Most spacecraft aren't intended for combat use.  Usually the (relatively) low thrust high efficiency engines are all anyone ever wants or needs.

Just make engine power modifiers slightly more expensive as a trade-off for allowing a x2EP engine to only consume as much as a x0.5EP engine if you dial the task-group down to 1/4 of full speed, instead of just consuming a quarter of normal consumption. I highly doubt rockets actually work that way in real life, but at least this way nobody needs to add any more buttons to the UI or any more mechanics that I need to use my calculator for.

Edit: Anyway, I don't like the comparisons to sea ships. TN elements might give the motion of this game's starships fluid-like characteristics, but these "ships" are still single-stage rocket vehicles and not boats. iirc the space shuttle itself only had one type of main engine (three of them), and anything else that it had was either intended to be jettisoned or it was a manoeuvring thruster.

What should such a button do? "Pick the speed for the task group that every ship can achieve on their least powerful engines" ? Something more user-definable?

If I were setting it up, I'd add a third speed box to the TG window, labeled 'cruise speed'.  It's user-definable, like the current speed box, but probably with a button that would set its value to 'maximum cruise speed for slowest ship'.  And add a command to allow you to set cruise and max speed through the orders window.

I'd care about having to do micromanagement to avoid wasting fuel for the same performance.

That's what is likely to kill this off.  High transit speed is a boon for most ships.

Using more than one engine will never be efficient due to the additional weight, wha I would prefer is if the currently existing option to change a task groups speed would also allow more efficient engine operation.

I'm broadly in agreement, although I can think of a few cases where a 'sprint engine' might be very handy.  The most obvious is for something like a survey vessel.  It's got a relatively slow main engine for its normal job, and a small, max-boost sprint engine for running away from things. 
 

Obviously an engine will be at its best operating condition when running at it's designed speed, just like a real engine, but there should be some advantage of running slower.  At the moment halving a ships speed just makes it take twice as long which uses just as much fuel.
You shouldn't be able to throttle back an FAC's engines to suddenly make them as efficient as a freighter, but going slower should save fuel, the question is how much?

The best way to do it is probably to change the 'resistance model' the game uses, not the engines themselves.  If power required scales with speed^1.5, throttling back will help a lot.  Allowing really wide throttling of the engines seems both unrealistic and an invitation for micromanagement and abuse.

Nice simplification. I think failure rate should be really high though so that it's a pretty risky combat maneuver.
The other important consideration is should NPRs be able to do this too? Of course you will say, it's cheating if you have another strategy to use against the AI which it can't counter.
Think of the possibilities, your hunter killer ships pounce apon those defenceless enemy freighters, only to find them pumping upto max power and evading your sleek new warship. Ok that's a problem, in some cases it should be possible, but certainly a .3 multiplier ship shouldn't be able to pump upto x3, an idea might to be make using this for power increase drops the ships commercial design flag, opening it up to failures, this would be very useful for Q-ships indeed. Maybe there should be a limit, maximum increase or decrease should be limited to how much multiplier you have researched. If you have 2x researched you can get a power 1 to power 2, or a power .5 to power 1 but not anymore than that.
The other consideration is that NPRs don't use fuel or maintenence so in theory their ships can just blast along at full overdrive with no worries, while your own ships run out of fuel and break.

Using more than one engine will never be efficient due to the additional weight, wha I would prefer is if the currently existing option to change a task groups speed would also allow more efficient engine operation.
Obviously an engine will be at its best operating condition when running at it's designed speed, just like a real engine, but there should be some advantage of running slower.
At the moment halving a ships speed just makes it take twice as long which uses just as much fuel.
You shouldn't be able to throttle back an FAC's engines to suddenly make them as efficient as a freighter, but going slower should save fuel, the question is how much? Related yo this perhaps you could throttle above 100% but at severe risk of failure?
Let's consider the normal power curve, going from 100% to 300% increases fuel use by 15 times, would it be acceptable to allow any engine the ability to do this again, also increasing failure rate by the same amount?
What about the opposite, I don't recall the exact mechanic but I think you can go down to .2 power and get the a 20th fuel consumption. If this was enacted as well then it would be trivial to lower an engines power even further for stupidly efficient freighters, or military vessels with anemic engines of negligible failure rate.
I think a good compromise would be to allow any engine to throttle up or down towards the currently existing limits, .2 or x3, but with an efficiency curve that's altered. This way you wouldn't get more powerful engines since the current max power already push the limit of what's possible, or more efficient engines as the same applies, but you gain flexability with median powered engines.
The question is how should this be balanced? Say you're using an engine with 1.0 power multiplier and have researched a max power of x3.
Obviously an engine actually designed to operate at that power is more efficient, perhaps increasing fuel use and failure rate by an additional 50% per level, and for reduced speed the opposite by decreasing the extra efficiency by 50% per level.
After designing the ship you send it out to battle and come across an enemy armada, you're outgunned and outclassed. The captain orders the overdrive setting. Which will enable it to outrun the enemy.
What happens?
Let's imagine the ship was designed for decent range, maybe 60 billion kilometres, not particularly good for a scout but fine for a warship.
If normal engine consumption was used we find that after going to overdrive the ship now has 3 times the speed and 15 times consumption. Range has dropped to 12 billion kilometres, which is still ample to outrun an enemy, even through multiple systems. But it's unfair to allow any engine to do this since the engine isn't running at its designed power, it should be less efficient.
What if we increase fuel consumption by the proposed 50% per level? Power levels increase at a rate of 25% more per level up to 3 times so from 1.0 to 3.0 is 8 levels, that's 4 times additional fuel consumption. A total of 60 times what the standard engine uses, but only 4 times less efficient as the properly designed engine of that power.
That range of 12 billion drops to 3 billion.
What if the inverse was true?
I can't remember the vanilla efficiency gains for less power so I'll leave this untill later, but if you start with a 3.0 power engine and decide to throttle it back using the above mechanics the instead of getting a 1/15th fuel consumption for a third the speed instead you multiply the vanilla efficiency change by 1.5 per level as before. So 8 levels gives an increase of 4 times of the vanilla 1/15 efficiency of an engine running at 1.0.
A third the speed gives you 26% the fuel use. Actual fuel efficiency gain isn't much in this example, you'll use 86% as much fuel to get there 3 times longer. But reducing power even further would give better efficiency gains.

I guess one solution would be for the engines to automatically prioritize using engines with the lowest Fuel Use Per EPH first, so if a ship is moving at the cruising speed, it would use exclusively the cruise engines, even if it is in "high speed mode", but if it only moves slightly above cruising speed, then it'll have it's cruising engines at full power, and it's high speed engines firing only to make up the difference.

That's what I was assuming.  The problem is that you're going to be spending a lot of time at lower than maximum speed, and it would be very helpful to have some way to semi-automate that instead of having to remember what your cruising speed is and then manually input it every time.

Now that I think of it: even if we don't allow multiple engine types powered at once, we can eliminate micromanagement by assuming that we can alternate between engines within a tick - after all, there is no inertia. So there would be a smooth progression for fuel consumption for both approaches.

That doesn't eliminate micromanagement.  The micromanagement is that you have to control speed a lot more closely under this approach.  Particularly if we go with only allowing one engine to run at a time, we need to have a button which sets the ship to its cruising speed.