This functionality is not available out of the box. But it's something people have been asking for (repeatedly) since at least D6 CCK 2:

* [Enable 'add more' button for non-unlimited fields.](http://drupal.org/node/344587)
* [Provide "Add more values" button for fields (and multigroups) with fixed number of multiple values](http://drupal.org/node/530828)
* ['Number of repeats' uses 'Add more' button](http://drupal.org/node/576540)
* ["Number of Values to Display" option for CCK fields](http://drupal.org/node/483198)

User [goron](http://drupal.org/user/359162) has developed a contrib module for Drupal 7 called [Multivalue Settings](http://drupal.org/project/multivalue_settings).

But be aware - from the module description page:

> Warning: this module is still very buggy. Actually, it only works in
> very few use cases. I suggest to only attempt using it with core
> fields (not fields from contrib modules). Even this may not work. I'm
> working on fixing things, but don't have much time. Help is welcome.
> If you're interested in helping make this module work, please contact
> me.

And it hasn't been updated in over a year.

**Screenshot of [Multivalue Settings](http://drupal.org/project/multivalue_settings) functionality:**
![enter image description here][1]


  [1]: https://i.sstatic.net/5LEyl.jpg