Put someone off/on something

Today, I learned that 'put someone off something' can mean "to make someone not want to do something, or to makesomeone not like someone or something", then, can I use "put someone on something" to mean the opposite of "put someone off something"?

1. We don't want to put our guests off staying with us overnight.

2. I put him off the idea of going shopping with me.

3. We want to put our guests on staying with us. overnight.

4. I put him on the idea of going shopping with me.

I made 3 and 4 from 1 and 2.

I wonder 3 and 4 make sense and natural, and if so, what could they mean.