This paper explores the relationships among product, process and organizational innovation, examining the complementarities-in-performance between these forms of innovation, within a supermodularity framework. Drawing upon two large samples of French and UK manufacturing firms using CIS4 (2002-2004), we explore whether firms can find a beneficial interplay between different forms of innovation. Since unconditional tests are often inconclusive about these complementarities, we implement a new procedure testing pairwise relations conditional on the presence/absence of a third form. Using this approach, we find conditional complementarities between product and process innovations in French and UK firms and between organizational and product innovations in French firms, but no complementarities between all three forms of innovation. Using different sub-samples, we show that the presence of complementarities depends on the national context as well as on firm size and firm capabilities, which gives support to the contingency perspective.