The future of computing requires heterogeneous integration, including the recent adoption of chiplet methodology, where high-speed cross-chip interconnects and packaging are critical for the overall system performance. As an example of advanced packaging, a high-density interconnect (HDI) printed circuit board (PCB) has been widely used in complex electronics ranging from cell phones to computing servers. A modern HDI PCB may have over 20 layers, each with its unique material properties and geometrical dimensions, i.e., stack-up, to meet various design constraints and performance requirements. Stack-up design is usually done manually in the industry, where experienced designers may devote many hours adjusting the physical dimensions and materials in order to meet the desired specifications. This process, however, is time-consuming, tedious, and suboptimal, largely depending on the designer’s expertise. In this article, we propose to automate the stack-up design with a new framework, ISOP+, using machine learning (ML) for inverse stack-up optimization for advanced package design with adaptive weight adjustment and multilevel optimization. Given a target design specification, ISOP+ automatically searches for ideal stack-up design parameters while optimizing performance. A novel ML-assisted hyperparameter optimization method is developed to make the search efficient and reliable. Experimental results demonstrate that ISOP+ is better in figure-of-merit (FoM) than conventional simulated annealing and Bayesian optimization algorithms, with all our design targets met with a shorter runtime. We also compare our fully automated ISOP+ with expert designers in the industry and achieve very promising results, with orders of magnitude reduction of turn-around time.