Pre-amp amplifier driving capacity

Don't laugh, how many amplifiers can one pre-amp drive? My system includes a pre-amp that drives normally two Hafler 220s and a 120, and sometimes I add in a homebuilt Marchand amp for surround. I may want to add another amp for the hell of it (a Moscode 300). Never noticed any degredation in the sound or overload problems. I'm not an engineer, I may not know very well what I do...
Since you don't want to share the brand and the model of your pre-amp, you will have to calculate it yourself.

Lookup the output impedance for your preamp, and the input impedances of all the power amps.
Then make sure that the total parallel input-impedances of all the connected power-amplifiers, is at least 5 times higher ( as a rule of thumb) than the pre-amps output impedance.
The sum of all the output cable capacitances could cause problems,
if excessive for the preamp's current capability.
Cable capacitance and RF attenuation capacitance needs to be summed.

The current required to drive the cable is usually more than the current required to drive the resistive load impedance.
4 channels of 10k for Rin driven to a maximum of 3Vpk (2.121Vac) draws just 1.2mApk
4 cables , each of 1nF of cable capacitance will draw 1.5mA, on a fast 20kHz transient.
Practical Line-Driving Current Requirements

This is a current capability problem.
Matching of impedance ratios for voltage drive efficiency is not the problem.
These two replies are looking at the wrong problem !
As long as the output impedance
the output impedance for your preamp, and the input impedances of all the power amps.
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Thanks everyone (and Andrew in ancestors are from Glasgow..I was named after some guy from the 13th century who is/was something of a hero.)
I have a Heathkit AP 1800 pre-amp driving the Haflers through one 30 foot balanced coax cable. The amps are "daisy-chained" together with Y-connectors.
I can determine all the necessary impedances etc. from the manuals I still have for the components. I don't have the equipment to measure capacitances though. When I get my Moscode 300 fixed, I'll hook it into my system somewhere and see what happens...
Wow, that preamp must have transistor output to drive all that.
My 12AX7 plate output preamp starts losing highs at anything over 6' of RCA cable.
Cable manufacturers list picofarad per foot in the catalog, but nobody with a supplier with an english language catalog hand wires RCA cables so the number is a bit obscure for that coax wire product.
Mixers also run against this cable capacitance problem. Home use mixers can use 4558 op amps with low current drive. Pro mixers that have a cable run of 100' to the stage power amps use higher drive current 4580 op amps for output.
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You could build an awesome splitter/buffer and drive as many power amplifiers as you want.

Some pro (sound reinforcement) power amplifiers have a buffered line out so you can daisy chain as many amplifiers as you want without worry.

In reality, a solid unbalanced buffer will drive several paralleled amplifier inputs through a reasonably long cable without worry. Low output impedance is a must. If there is a capacitor coupled output you must make sure you don't drive the F3 up too much. Three 47K input impedance amplifiers in parallel is 15.7K which shouldn't be a problem for a solid state preamplifier. A 4.7 uF output capacitor would yield an F3 of 2 Hz in this example, which is fine.