Is it possible to add unlimited values as a group of fields?
For your use case, there is the Field Collection module. The description given in its project page is the following.

Provides a field-collection field, to which any number of fields can be attached.
A field collection is internally represented as an entity, which is embedded in the host entity. Thus, if desired field collections may be viewed and edited separately too.

The latest stable release for Drupal 7 is 7.x-1.2, released on December 26, 2020; it's not covered by the security advisory policy. The development snapshot for that release has been last updated on March 26, 2021.
For Drupal 8, the project maintainers suggest using a different module.

Use Paragraphs and Entity Reference Revisions instead of field collection for Drupal 8 projects.

Since one of those modules doesn't have a release for Drupal 7, that suggestion isn't for users who are running Drupal 7 sites.