Moodle DOES allow multiple graders for the same assignment - but only the LAST grade posted anyone of the graders is the one that gets shown in the gradebook/grading system. In other words, the last teacher to enter a grade, overwrites any other grade already there.
Depending on what you are doing in the "assignment" is there any possibility of doing it in the database, glossary, or forum activities? (Any kind of writing assignment would work great.) Each of those use a rating system that can be set for average of rating, then grades from multiple graders will be averaged into the grade book. The last grade entered by each grader is what is used in the average. In other words, each teacher will have only their last grade used in calculating the average. You also have the advantage of being able to set the rating for maximum, minimum, sum, or count of the ratings.
If, by chance, you are wanting to grade audio and or video, the Podcast addon, also uses the rating system.
One other possibility, have you thought of trying to use the Workshop activity? Even though it uses peer rating, your multiple graders could be added, just not submit anything and rate all the student submissions. You would probably need to use manual allocation for who grades what. I haven't tried this so not absolutely sure it would work exactly like you want.