What is an alternative to Dictionaries in C# that allows for duplicate keys?

In your case, the same key is related to multiple values, so standard dictionary is not suitable, as is. You can declare it like Dictionary<Key, List<Values>>.

But, also, you can use:

Lookup class, which is

Represents a collection of keys each mapped to one or more values.

You need framework 3.5 and more, for this.

What you need is a relationship between a Project and one or more Technicians:

public class Project
{
    public ICollection<Technician> Technicians { get; set; }
}

var project = new Project();
project.Technicians = new List<Technician>()
{
    new Technician(),
    new Technician()
};

Your objects should mirror the relationships in real life.

As a side note, you might be interested in reading about Domain-driven design.

public void LoadTechnicians(Project project)
{
    List<Technician> techs = new List<Technician>();

    // query the database and map Technician objects

    // Set the "Technicians" property
    project.Technicians = techs;
}

There is an experimental NuGet package from MS that contains MultiValueDictionary.

Basically, it's like Dictionary<Project, List<Technicians>>, except that you don't have to repeat all the logic to manage the Lists every time you access it.