it's possible but you'll need to be careful how you wire it. the easiest way probably would be to buy two 16ohm speakers and one 8ohm speaker. wire the two 16 in parallel and the run them in series with the 8 ohm and BAM you got yourself a 16ohm 3 x 12 cabinet.
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watch out for power ratings. is the two 16 ohm speaker handle 100 watts, then one ohm speaker must handle 100 watts on its own
Yes, it can be done. Don't be surprised when it comes out sounding a lot worse than a 2x12 and a 1x12 connected in series.
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i would say to make a 2x12, and if you want later, another 2 or 4x12 and use the original as an extension cab
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Possible? Yes.
Sensible? Probably not.

Even if you connect the way shredzilla suggested, you'll have the power being divided unevenly between the speakers. the 8 ohm speaker would get twice the power that each of the 16 ohm speakers does. this is not only a concern for choosing the power rating of the speakers, but also on what each speaker will be doing. if they're all the same efficiency, the 16 ohm speaker will be doing the same amount of work as the other 2 combined.

so the question isn't could you do this, it's you should do this?
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you could maybe do something similar, well it wouldn't be similar, but it would use 3 speakers in one cab

put 2 10" and a 15", like they do in those bi-amping circuits, and run both speaker outs from your amp through them.

the 15" would want to be pretty high power handling though, depending on what amp you have
Seems like it would just be easier to do a 4x10". I think that would be the more sensible option and then save more money.
Um, I know a guy in town who gigs one with his orange head and it sounds amazing, if you did it correctly, it would be awesome and sound great
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Install speakers with the same impedance. You'll get a mismatch with your amp's output impedance, but it will be close enough.