Hi

The short answer is no.

The longer answer is:

I don't have a Spider IV 75.  I have a Spider IV 150.  The connections at the rear of my Spider IV 150 include a Left and Right speaker output.  I know that if I use an external stereo (or two mono cabs) speaker cabinet of the correct impedance (8 ohms per side) that the internal speakers are disabled to protect the amp from being overloaded.  Not being a Spider IV 75 owner I'm not 100% sure whether you even have a speaker output socket on the back of your amp - and none of the manuals for the Spider IV 75 show the back panel for a Spider IV 75.  I strongly suspect your amp doesn't have a speaker output jack though, so if that is the case, without modifying the speaker output leads attached to your amp's speaker, and possibly changing your amp's speaker depending on what sort of extension cab you want to use, the answer is still no.

The speaker in your amp is an 8 ohm speaker.  The amp is designed to provide 75w of power into an 8 ohm load and no less than that.  If you were to attach another 8 ohm speaker in parallel with the internal speaker, the speaker impedance load presented to the amp would be 4 ohms and that being the case, the amp would try its best to become a 150w (approx) amp but unfortunately the internal components would find the strain too much and the output module would simply burn out.    You would have to change your amp's internal speaker to a 16 ohm model and then use an external speaker cabinet with a load of 16 ohms in parallel with your amp's internal speaker to maintain the required 8 ohm speaker load.   IF you do want to use say an external 2x12 cabinet as well as an internal speaker, the internal speaker would need to be 16 ohms and the external speaker cabinet would have to have a total impedance of 16 ohms too (two 8 ohm speakers in series).   If you just wanted to use an external cabinet you would need to disconnect the internal speaker and tape up the contacts on the speaker wires to be safe so they can't touch, then you'd connect your 8 ohm external cabinet to your amp's speaker jack if it has one - or if it doesn't, you'd need to connect the external cab directly to the speaker wires you've just taped up.

If you swapped your amp's speaker for a 16 ohm model or tried to add an external cabinet  by running wires from the existing speaker wires, the configuration would not be supported or recommended by Line 6 and if you accidentally fried the amp, your warranty would be invalidated.   You could probably run your amp with a 16 ohm single internal speaker without problems being caused to the amp itself, but it would only run at half power (37.5w) and for obvious reasons you wouldn't really want to do this as you are I believe after more volume rather than less.

Would adding an external speaker give your amp more volume?  Your speaker configuration would potentially give your amp the ability to move twice as much air, but the amp's power would be spilt equally between the two speakers, so neither speaker cone would move quite as far individually.   In practice you would probably notice a very slight increase (and I DO mean VERY slight) in overall volume and slightly less distortion if you used two speakers rather than one, but the difference in volume would hardly be noticeable to the human ear.  i think you would be more likely to notice a difference in the amp's tone than a significant rise in volume, which  may or may not be a good thing :-)

Would it be worth the effort and extra expense as well as the risk to your amp?  Realistically, probably not IMO as you'd probably need to swap out your amp's speaker for a 16 ohm model and what you'd get for your money probably wouldn't warrant the expense.

If you really want more volume, your preferred options would be to buy a Spider IV 150 combo or head and cabinet, or to buy a Spider Valve MkII 212 40w combo (valve amps are perceived as significantly louder per watt than solid state amps are in general) or HD100 head plus cab.  The Spider IV 150 combo is a seriously loud amp as it stands.

Nick