If you have a sound argument, and then add a new premise, will the argument be sound, unsound, or either?

Does the same apply for a valid argument? - in the example below, i tried to suggest that the argument on the left with the new premises (3,4) is invalid, whereas the original is valid.

Uluru is a landmark in Redfern Uluru is a landmark in Redfern
Redfern is in the centre of Australia Redfern is in the centre of Australia
Redfern is an island republic Uluru is an Australian landmark - Valid
Australia is comprised of a donut shaped landmass
Uluru is an Australian landmark - Invalid

any thoughts, help, etc is appreciated

i dont think i particularly understand what your saying with your example, but i think it would become unsound due to the new "rule" making a previous rule incorrect

the fourth rule would immediately make the second rule incorrect. because you have conflicting evidence to prove a point, you wouldnt have a sound argument. i think

btw, are you Harry_Hardcore_Hoedown?

I think I understand your question. Your example is poorly constructed though, so if you don't mind, I will set up my own to talk about.

1. ¬(A&B)
2. A
3. B
# ¬B (deduced from 1. and 2.)

The deduction is quite valid, because it follows from 1. and 2. However, it results in an inconsistent set, and this means one of three things: the argument is sound and therefore 3. is untrue, 3. is true and therefore the argument is unsound, or 3. is untrue and the argument is unsound.

you can add however many premise(s) you want to an argument, sound or valid or vice versa, and it can come out as being sound, valid, or vice versa. it all depends on the premise(s) you add to the argument.

i.e.
1. socrates is a man.
2. all men are mortal.
3. therefore, socrates is mortal.

add in however many premises you want to this.

1. socrates is a man.
2. all men are mortal.
3. all men breathe in and out air.
4. no men are able to fly.
5. therefore, socrates is a mortal who breathes in and out air and cannot fly.

the premises i added keep the truth connections, and you can add more still, though they might not keep the truth connections. just make sure the conclusion is shaped in such a way as to make the argument valid from the premises you added.