Multiple instances one same web app

Hi everybody,

I have an app that is accessed by different companies. Each company
has a separate database but I want to have only one web app.

Today I have to create one web app to each company to use each
web.config to point to the right database. The user when logging in
selects the company id and each company has a folder/app copy with
it's own web.config.

Can I have only one web.app that has multiple web.config? Is this
correct or is it a bad practice? I was thinking if is possible to have
one bin folder and in someway point to a web.config that has the
configuration for the desired company.

I don't know if I made it clear enough, so tell me if you get it
right.

Thank you very much.