Neural-like P systems with plasmids (NP P systems, in short) are a kind of distributed and parallel computing systems inspired by the activity that bacteria process DNA such as plasmids. An important biological fact is that one or more pili have existed between two neighboring bacteria during the conjugation process, and this phenomenon can be abstracted into the concept of multiple channels. In this paper, we raise a type of distinctive P system that the neural-like P systems with plasmids and multiple channels (NPMC P systems, in short). In NPMC P systems, one or more channels are established between neighboring bacteria, each channel marked by the associated label is used to control the communication between two bacteria. Rules are applied in sequential order: each channel can only have one rule applied at a time. The computation power of NPMC P systems is explored. In particular, we show that NPMC P systems satisfy Turing universality in both the generating and accepting modes. If we limit the number of plasmids in any bacteria during a computation, then the power of NPMC P systems decreased drastically, but the characterization of semilinear sets of numbers is obtained (SLIN, in short).