Treatment effect estimation is crucial for making reliable decisions and avoiding spurious correlations. However, estimating causal effects is harder in limited unbalanced observations, particularly in decision-making systems with multiple causes like healthcare, and politics. In this paper, we aim to enhance the estimation of the multi-cause conditional treatment effect (M-CATE) by augmenting limimted observational data with interventional data to alleviate the data unbalancing. One challenge is that the distribution of interventional data may not be close to the real data. We leverage the causal graph to consider the relationships among causes to solve this. Another challenge is that general identification conditions do not satisfy the realization of intervention. Thereby we give milder partial-cause conditions for identification to construct a Partial Cause Intervention (PCI) algorithm for M-CATE estimation. Specifically, we first intervene in part of the causes once at a time through causal regression which means only modeling the predicted variable using its parent variables, and then we combine the limited observational data with all the interventional data for M-CATE estimation. To support our approach, we prove that the estimation error can be upper bound by the empirical error and the distributional shift among treatments. The experimental results in simulations and real-world data applications validate our approach and theoretical findings.