The article proposes and theoretically analyses a computationally efficient multi-task learning (MTL) extension of popular principal component analysis (PCA)-based supervised learning schemes. The analysis reveals that (i) by default, learning may dramatically fail by suffering from negative transfer, but that (ii) simple counter-measures on data labels avert negative transfer and necessarily result in improved performances. Supporting experiments on synthetic and real data benchmarks show that the proposed method achieves comparable performance with state-of-the-art MTL methods but at a significantly reduced computational cost.