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We are motivated by the question that for which class of right-angled Artingroups (RAAG's), the quasi-isometry classification coincides withcommensurability classification. This is previously known for RAAG's withfinite outer automorphism groups. In this paper, we identify two classes ofRAAG's, where their outer automorphism groups are allowed to contain adjacenttransvections and partial conjugations, hence infinite. If $G$ belongs to oneof these classes, then any other RAAG $G'$ is quasi-isometric to $G$ if andonly if $G'$ is commensurable to $G$. We also show that in this case, thereexists an algorithm to determine whether two RAAG's are quasi-isometric bylooking at their defining graphs. Compared to the finite out case, as well asthe previous quasi-isometry rigidity results for symmetric spaces, thickEuclidean buildings and mapping class groups, the main issue we need to dealwith here is the reconstruction map may not have nice properties as before, ormay not even exist. We introduce a deformation argument, as well as techniquesfrom cubulation to deal with this issue.

Quasi-isometry classification of right-angled Artin groups II: several infinite out cases