Can I connect multiple speaker boxes to a single amplifier output?
Yes, you are correct, you should not connect a speaker (or speakers) whose total impedance is less than the rated amplifier output.  If the equivalent speaker impedance is higher than the amplifier output (e.g. connecting  an 8 Ω speaker to an 4 Ω amplifier output). then the output will not be as loud as it could be

If you are connecting up more than one speaker to an amplifier, then you can create a network of parallel and series speaker connections to keep the impedance equal to or higher than the amplifier output.  



In large installations, such as a sports arena where there may be hundreds of speakers, that's not what they do.  Instead they use a "high-impedance constant voltage" distribution scheme:



A transformer at the power-amplifier output steps up the voltage to approximately 70.7V at full power. Each speaker has a step-down transformer that matches the 70.7V line to each speaker's impedance. Each of the step-down transformers are wired in parallel, making it trivial to add or remove speakers on the system.

Another advantage of this type of system, is the 70.7V line reduces power loss due to  cable heating. That's because the speaker cable carries the audio signal as a low current. Therefore you can use smaller-gauge speaker cable or a very long cable.

The disadvantage of this scheme are the extra transformers needed; however it is possible to get both amplifiers (like the one below) and speakers that already included the needed step-up/step-down transfers.

 

The 25V output shown next to the 70V one is an older standard.  You may also see 100V systems.