Generally, the heliospheric current sheet (HCS) is separated from the stream interface (SI) at about 1 AU. A recent study found an event where the HCS coincides with the SI, and in which the HCS is separated from the true sector boundary (TSB), defined by the switch of suprathermal electron pitch angle distributions. We present a multievent study by using STEREO, ACE, and Wind data during 2007 to 2010 to investigate whether other classes of such coincidence cases exist, as well as their stability. We find coincidence cases related to ideal HCSs, separated TSB and HCS, or heat flux dropouts in the vicinity; therefore, we define them as types I, II, and III. Among the nine coincidence cases, there are seven type I, one type II, and one type III. For each type, a possible schematic origin is presented. We also compared the observations on different spacecraft. Only two out of nine cases are observed by several spacecraft with a large separation, indicating that the coincidence structures are usually unstable. The study also shows that the coincidence cases have a variable connection with pseudostreamers. Interchange reconnection and pseudostreamers could play a role in forming these coincidence cases and lead to different configurations in different situations.