Yes, it is certainly possible. Apple should not reject you for this purpose. It is entirely allowed to have different branding, color schemes, etc. according to the logged in user.
You can find the App Store review guidelines here:
As you'll see there's no section that explicitly allows nor forbids what you want to achieve. This means that what you want to do would normally be considered OK. Make sure that you comply with section 5.2 and do not use intellectual property (logos, branding text, etc.) that is not your to use.
However, if you also offer different functionalities - make sure that you supply the Apple review team with all the functionalities. It is not permitted to have the app reviewed with one set of functionalities, and then let users have a completely different set of functionalities in the app after they login with a specific "secret" set of credentials.
Also make sure to comply with section 3.1.1 about In-App Purchases, if you want the user to not only have different branding but also have different functionalities after login.
The screenshots on the App Store does not have to display all and every type of branding or color scheme possible in the app. There's no requirement for that, so you should not have problems here. However, the screenshots must be a true representation of the app itself - i.e. for example take screenshots of one of the color schemes / branding and use that. I.e. do not use screenshots that are different from what is actually possible to get within the app if you have the right credentials.