Certain example embodiments of this invention relate to coated articles with low-E coatings having one or more barrier layer systems including multiple dielectric layers, and/or methods of making the same. In certain example embodiments, providing barrier layer systems that each include three or more adjacent dielectric layers advantageously increases layer quality, mechanical durability, corrosion resistance, and/or thermal stability, e.g., by virtue of the increased number of interfaces. These barrier layer systems may be provided above and/or below an infrared (IR) reflecting layer in the low-E coating in different embodiments. Coated articles according to certain example embodiments of this invention may be used in the context of insulating glass (IG) window units, vehicle windows, other types of windows, or in any other suitable application.