This is an open label, dose finding, phase Ib clinical trial to determine the maximum tolerated dose (MTD) and/or RP2D of the orally administered PI3K/mTOR inhibitor BEZ235 in combination with the MEK1/2 inhibitor MEK162. This combination will be explored in patients with EGFR mutant NSCLC which has progressed on EGFR inhibitors and triple negative breast cancer, as well as pancreatic cancer, colorectal cancer, malignant melanoma, NSCLC, and other advanced solid tumors with KRAS, NRAS, and/or BRAF mutations. Dose escalation will be guided by a Bayesian logistic regression model with overdose control. At MTD or RP2D, two expansion arms will be opened in order to further assess safety and preliminary anti-tumor activity of the combination of BEZ235 and MEK162.