In many industries, multiple independent complementors supply the individual components of a system. In this paper, we develop a formal model to examine the tensions and tradeoffs that result when a firm-either one of the complementors or a de novo entrant-takes competition to the system level by launching an integrated offering that combines the multiple components. A complementor who takes competition to the system level becomes a competitor to itself at the system level. As a consequence, the task of maintaining the competitiveness of the multiple-component system rests on the shoulders of the remaining complementor. We show that this allows the integrator to earn additional profits at the expense of the complementor-that is, it can raise the price of its component and thereby squeeze the margin of its complementor. We find that this squeezing effect can be so strong that offering an integrated system is profitable even if the system itself is unprofitable. Interestingly, when analyzing the possibility of entry by a de novo integrator who does not suffer from self-cannibalization, we show that an incumbent complementor may nevertheless have stronger incentives to launch an integrated offering. This is because the incumbent's ability to benefit from squeezing its complementor and earn additional profits on cannibalized sales leads to an entrant's disadvantage when taking competition to the system level. We also discuss defense strategies for complementors to shield themselves against the consequences of integration by their complementor.