J. L. Verdier dissertation covers  multiple-graded  complexes.

>Des catégories dérivées des catégories abéliennes. (French. French summary) [On derived categories of abelian categories] 
With a preface by Luc Illusie. Edited and with a note by Georges Maltsiniotis. 
Astérisque No. 239 (1996), xii+253 pp. (1997).