I can't say authoritatively, as it's been a while since I worked on an iMac, but I'm pretty sure that there is only one internal SATA port, for one drive. Newer ones may well have the SSD soldered to the board, and may not be replaceable (I know this is the case with Macbooks now).
If it is replaceable, you're correct in thinking that you could replace it with a drive of greater capacity, but bear in mind that iMacs with removable drives have a thermal sensor cable that is hot-glued to the drive. I don't know if a different type of drive will affect the thermal readings on your particalar model, and whether or not this will affect what the iMac thinks is going on.
I reckon it will be fine - you can probably just tape the sensor back in place (better to hot glue it, though). I've replaced iMac HDDs with SSDs several times before now, with no ill effects, but I can't say for definite about yours.
With Apple stuff, there is always some idiosyncratic problem waiting to throw a spanner in the works if you mess with it too much, but I'm 90% sure you'll be ok with the drive replacement. Look on YouTube for '>your model< drive replacement'. There are usually loads of vids about this kind of thing.
If you need a second drive, external is probably the way to go.
PS you will need to remove the magnetically held glass screen to get into it. The suction cups on dashboard phone brackets are the best thing for this. A pair will do the job nicely.
PPS Beware of tearing or damaging the foil EMI shield! See my bad exeprience here: Why is Airport receiving only weak signals after HDD replacement?
You might need to purchase foil tape to repair it if it becomes damaged.