In the third Galactic quadrant (180° ≤ l ≤ 270°) of the Milky Way, the Galactic thin disk exhibits a significant Warp-shown both by gas and young stars-bending down a few kiloparsecs below the formal Galactic plane (b = 0°). This warp shows its maximum at l ∼ 240°, in the direction of the Canis Major constellation. In a series of papers, we have traced the detailed structure of this region using open star clusters, putting particular emphasis on the spiral structure of the outer disk. We noted a conspicuous accumulation of young star clusters within 2-3 kpc from the Sun and close to b = 0°, which we interpreted as the continuation of the Local (Orion) arm toward the outer disk. While most clusters (and young stars in their background) closely follow the warp of the disk, our decade-old survey of the spiral structure of this region led us to identify three clusters, Haffner 18 (1 and 2) and Haffner 19, which remain very close to b = 0° and lie at distances (4.5, ∼8.0, and 6.4 kpc) where most of the material is already significantly warped. Here, we report on a search for clusters that share the same properties as Haffner 18 and 19, and investigate the possible reasons for such an unexpected occurrence. We present UBVRI photometry of five young clusters, namely NGC 2345, NGC 2374, Trumpler 9, Haffner 20, and Haffner 21, which also lie close to the formal Galactic plane. With the exception of Haffner 20, in the background of these clusters we detected young stars that appear close to b = 0° and are located at distances up to ∼8 kpc from the Sun, thus deviating significantly from the warp. These populations define a structure that distributes over almost the entire third Galactic quadrant. We discuss this structure in the context of a possible thin disk flaring, similar to the Galactic thick disk.