polite enquiries

[ostap77]

Can we use a progressive form of "going to" structure to make polite enquiries about people's plans?

"Will you be staying in this evening?" I simply want to know plans.

OR

"Are you going to stay in this evening?" We want to get an answer.

OR

"Are going to be staying in this evening?" Possible? What would be the meaning?

 

[Raymott]

Can we use a progressive form of "going to" stucture to make polite enquiries about people's plans?

"Will you be staying in this evening?" I simply want to know plans.

OR

"Are you going to stay in this evening?" We want to get an answer.

OR

"Are going to be staying in this evening?" Possible? What would be the meaning?

Yes, you can use any of those forms. There's no difference in terms of politeness.
You can also say:
Are you planning on staying in ...
Do you plan to stay in ...
Do you plan to be staying in ...