I was just training someone on position the other day and this came up.
You CAN have more than one aircraft on the visual approach, but
you either have to keep them in trail and separated, or get the back
one to see the front and follow him in. The latter is not as simple
as it seems, as let's say you have one right behind another, by right
behind I mean at least 5 miles since that is our separation standard.
It's unlikely the trailing aircraft will see the other 5 miles (or more,
who runs a bare 5 with someone slowing in front) ahead, so you have
to use more and figure in compression. Thankfully there is no missed
approach on the front guy so you don't have to worry about him climbing
and maybe starting a 180 degree turn shortly after 'missing'.

Sometimes more space is built in where radar is questionable, or
at an uncontrolled field where landing/cancellation wont be immediate
like it would be with a tower, or if it's not a straight-in - time for
downwind,
etc.

The "following the preceding aircraft" thing is great, when you can get it,
mostly you cant. About the only way I get it to happen is to get them
real close, like one on a 5 mile final and one descending above him head
on, at night this works pretty good. The other way is to have one overtake
the other, but I have to keep vertical until visual takes over. Or if they
are somewhat matched speeds right behind each other, try to get em within
2 miles, again keeping vertical, get visual and clear the back one to follow
the front.

Here's why you'll get hesitation from the controller, at centers anyway:
Nearly every operation like I described above will set off the OEDP,
Operational Error Detection Program, or 'snitch', 'squeal a deal', whatever
you want to call it. That leads to a non-controller up front calling an
occasional controller, your supervisor, who then questions what you
are doing. Let's say one of those aint your best buddy and decides to
pull a tape and you leave one word out, or the readback was garbled
or the pilot read back everything right but one word, etc etc. This has
never happened to me, but you can see how some would rather not
deal with the hassle and just wait a few minutes more. Like it or not,
that's the reality of how it is.
Hope that helped, Chris