Commonsense knowledge graphs (CKGs) like Atomic and ASER are substantially different from conventional KGs as they consist of much larger number of nodes formed by loosely-structured text, which, though, enables them to handle highly diverse queries in natural language related to commonsense, leads to unique challenges for automatic KG construction methods. Besides identifying relations absent from the KG between nodes, such methods are also expected to explore absent nodes represented by text, in which different real-world things, or entities, may appear. To deal with the innumerable entities involved with commonsense in the real world, we introduce to CKG construction methods conceptualization, i.e., to view entities mentioned in text as instances of specific concepts or vice versa. We build synthetic triples by conceptualization, and further formulate the task as triple classification, handled by a discriminatory model with knowledge transferred from pretrained language models and fine-tuned by negative sampling. Experiments demonstrate that our methods can effectively identify plausible triples and expand the KG by triples of both new nodes and edges of high diversity and novelty.