Can someone unsubscribe from one email type from your account but not another?

[WGCU2019]

We send various types of emails as a public media station. A person who "unsubscribes" apparently receives no more emails from us. But they may be interested in a different type of email, just not the one they are trying to unsubscribe to. 

Is there a way to, say, have a form automatically appear when someone unsubscribes that asks exactly which subjects the person wants to no longer receive?

For instance, they may receive an email from us about a cooking show and not care at all about that. But we also send emails about new nature shows, and they may want those. 

[William_A]

Hello @WGCU2019 ,

By default an "Update Profile" link is included in all your emails' footers alongside the unsubscribe link (unless manually turned off in your Settings). These coded links are what your contacts can use to change what lists they want to be a part of, rather than wholly unsubbing from you. To change what list options are available for your UP form, you can edit it in the Sign Up Forms > Basic Landing Pages. Adding list options to your UP form should also allow them to be an alternative option when a contact clicks the unsub link.

For full details on Update Profile functionality