Trying to create different card types with cloze deletions

I’m trying to create a custom deck where there are several card types per note. I also want to use cloze deletions. However, when I try to create the card types in the options menu, there is no option to do it.

You cannot create additional card templates yourself on the native Cloze notetype.

To create a notetype that can do both normal Q&A and clozes, you can take a look at Closet For Anki - AnkiWeb or invent your own cloze syntax and use JavaScript.