With the increasing scarcity and cost of virgin materials for asphalt mixtures, the exploration of alternative components has intensified. Reclaimed asphalt pavement (RAP), crumb rubber (CR), steel slag (SS), and waste engine oil (WEO) have emerged as promising alternatives. Individually, RAP enhances rutting resistance but may compromise cracking tolerance; CR boosts cracking resistance; WEO affects cracking and rutting differently; and SS can influence moisture sensitivity. However, their combined impacts on asphalt performance, specifically on moisture damage, rutting, and cracking resistance, remain underexplored. In this study, 44 mixtures were assessed with varying RAP (0–75%), WEO (0–15%), and CR (0–15%) contents, alongside a constant SS aggregate (0% or 20%). The results indicate that specific combinations of these alternative materials can satisfy all performance thresholds for rutting, cracking, and moisture damage. To pinpoint ranges of optimal material contents for different high-traffic scenarios, prediction models were crafted using techniques like feed-forward neural network (FNN), generalized linear model (GLM), support vector regression (SVM), and Gaussian process regression (GPR). Among these, GPR demonstrated superior efficacy, effectively identifying regions of satisfactory performance.