Can you upgrade the space on a iPhone 4s?

I have a IPhone 4s 8gb but I need more space… Is there a part I can buy to change it for 8gb to 16 or 32gb?

No you can sell your iPhone and buy one with bigger gb

You could in theory yes, however it would in all likelihood be simpler to not risk breaking the iPhone (Apple makes this very easy if you try and open it up) so what I would recommend is you

1) sell your current iPhone

2) purchase your desired iPhone.

Although you will be marginally more out of pocket, you will be guaranteed an iPhone as opposed to having a broken iPhone and being even more out of pocket.

You gots to buy a new iPhone. There's no removable memory.