Carpet on carpet


I have my first property which I’m currently making tenant friendly before letting it out. I’ve had to put in a new bathroom, back door, and guttering. The walls and ceiling is currently being decorated. It’s a 2 bed terrace so acoustics are awful as expected.

Now I need to lay new carpet as the current one is v old and the house smells not so fresh. So my first thought obviously was to rip the carpets up.

But now, I’m wondering, can I lay new carpet on top of the old carpet? I’m thinking:
1/ saves on underlay
2/ will keep the house warmer
3/ helps to absorb sound a bit better.

I definitely have to rip the old carpet up on the stairs as they are too steep and it would be a death trap if it was left.

I’m also thinking similar in the kitchen and bathroom - put new vinyl on old vinyl.

Has anyone successfully done this? Thanks

do not do it the top layer will slip and wear out quicker