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We consider the problem of private multiple linear computation (PMLC) over a replicated storage system with colluding and unresponsive constraints. In this scenario, the user wishes to privately compute linear combinations of files from a set of replicated servers without revealing any information about the coefficients of these linear combinations to any colluding servers, in the presence of unresponsive servers that do not provide any information in response to user queries. Our focus is on more general performance metrics where the communication and computational overheads incurred by the user are not neglected. Additionally, the communication and computational overheads for servers are also taken into consideration. Unlike most previous literature that primarily focused on download cost from servers as a performance metric, we propose a novel PMLC scheme to establish a flexible tradeoff between communication costs and computational complexities.