It's possible, but first you have to have basic tables/relationships in place. If I am understanding your post correctly, you have a "many to many" relationship here. Presumably, a personnel record could be linked to more than one project and you've stated in your post that a project can have more than one personnel assigned to it at the same time.
This requires a Join table and these relationships:
Personnel::PersonnelID = Personnel_Project::PersonnelID
Projects::PRojectID = Personnel_Project::ProjectID
With this set up, you can put a portal to Personnel_Project on your Projects layout and use a drop down list in the portal to select values for the Personnel_Project::PersonnelID field. This can be a drop down list of ID's from Personel with a second field supplying the full name of the people listed in this table. This works for relatively small lists of personnel. With longer lists, it's possible to use more sophisticated designs that make choosing from a long list of names easier to manage.
To remove a person from a particular project, you'd delete the portal row in this portal--which deletes the record in Personnel_Project. In all of these operations, Personnel, is left unchanged.
Here's a demo file that illustrates this basic setup as well as two more sophisticated approaches designed to prevent users from making the same assignment twice for the same pair of records:
In the personnel file, I have first and last names as separate fields, but repeat last names. I can only have two fields in the drop-down menu and one of them has to be the personnel ID. What is a feasible solution to this problem?
Option1: Define a text field with an auto-enter calculation such as: LastName & ", " & FirstName. Use it as your second value in the value list. A calculation field can also be used for this, but using a text field allows you to specify validation rules such as requiring unique first/last name combinations--which can be useful when serving as a data source for a value list.
Option2: Don't use a value list. The Checkboxes layout in the demo file is an example of how to select records without choosing from a value list.
Awesome, you da man, phil.