Pipelining and Preemption
Your question reminds me of an old joke:

If the Atlantic can be crossed in 7 days with one boat, you can cross it in
one day, if you have seven boats available. (there are actually many variants)

Your problem is the problem of assembly lines in general, and that is the technical model of a pipelined processor.

On the assembly line for making car (I am of course simplifying), you
will have one fellow placing the doors, another one placing the
bumpers, one placing the wheels, another painting the car. They all
work at the same time, doing their job in the duration of a single
car making cycle, fixed by the big clock on the factory wall.

Every cycle, the last worker of the line finishes one car, while the first
does the initial steps of making a new one. So there is exactly one
car produced for each cycle. There is a single assmbly line (read:
a single processor), producing one car with each cycle. 

But it does not mean that it takes only one cycle to produce a car. It
takes as many as there are stages in the assembly line. The rate of
production (read processing rate) of one car per cycle is only a
average over time.

The idea that that it is more efficient to have specialized workers
working independently. But you do not want to keep them idle, when it
is not their turn on a given car.

And, it may not be necessary that each car is built identically to the
previous one. All you need is that each worker gets his part of the
instruction(s), such as the diameter of the wheels to be placed, or
the color of the paint. So the instructions may change, while going
through the same assembly line to produce cars.

No one ever preempts the line to get something done. But all contributing workers are synchronized.