We present results from a search for additional transiting planets in 24 systems already known to contain a transiting planet . We model the transits due to the known planet in each system and subtract these models from lightcurves obtained with the SuperWASP survey instruments . These residual lightcurves are then searched for evidence of additional periodic transit events . Although we do not find any evidence for additional planets in any of the planetary systems studied , we are able to characterise our ability to find such planets by means of Monte Carlo simulations . Artificially generated transit signals corresponding to planets with a range of sizes and orbital periods were injected into the SuperWASP photometry and the resulting lightcurves searched for planets . As a result , the detection efficiency as a function of both the radius and orbital period of any second planet , is calculated . We determine that there is a good ( > 50 per cent ) chance of detecting additional , Saturn-sized planets in P \sim 10 d orbits around planet-hosting stars that have several seasons of SuperWASP photometry . Additionally , we confirm previous evidence of the rotational stellar variability of WASP-10 , and refine the period of rotation . We find that the period of the rotation is 11.91 \pm 0.05 d , and the false alarm probability for this period is extremely low ( \sim 10 ^ { -13 } ) .