That's exactly what the [Features][1] module is for. Syncing partial config across multi-site instances.

> The features module enables the capture and management of features in
> Drupal. A feature is a collection of Drupal entities which taken
> together satisfy a certain use-case.
> 
> Features provides a UI and API for taking different site building
> components from modules with exportables and bundling them together in
> a single feature module. A feature module is like any other Drupal
> module except that it contains additional information in its info file
> so that configuration can be checked, updated, or reverted
> programmatically.

That means you would create a feature on your main multi-site instance that contains the paragraph type. Have it placed inside the modules/features/ folder. Related config will be added automatically. You then enable the feature on another multi-site instance. The config will be imported into the database. On both multi-site instances you then export config as usual.

As soon as you add another field to the paragraph type on either multi-site instance Features will recognise the changes. You then can recreate your paragraph feature and import the changes on another multi-site instance (into the database). Finally, on both sites again export config as usual (which then also contains the paragraph types you've synced via Features). Every multi-site instance still has its own config. Features enables you to keep track of changes to a feature via built-in diffing, which after you recreated the feature (partial config gets exported) can be synced into the database on other multi-site instances again.

Of course Features also comes with a set of Drush commands to make your live easier.

  [1]: https://www.drupal.org/project/features