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We investigate novel serially-connected multiple single-electron transistors (MSETs) as a single-charge polarisation readout for silicon integrated charge qubits. We first design and analyse the double single-electron transistors (DSETs) in which double quantum dots are connected in series with two side gates. We show that the DSETs are sufficiently sensitive to distinguish all the single-charge polarisation states on the two charge qubits integrated adjacently. We also show the scalability of the MSETs by extending our analysis to a scaled-up system of serial triple single-electron transistors (TSETs) integrated with triple charge qubits. Finally we fabricate the DSETs with double charge qubits on the silicon-on-insulator substrate and observe hysteresis in the Coulomb oscillations of the tunnel current at temperature of 4.2 K, which are attributable to the change of polarisation in the double charge qubits.