An auxiliary frame system for a wheelchair, the wheelchair having a frame comprising two openings to releasably attach axle portions of rear wheels and defining between them a main rear wheel axis; wherein the auxiliary frame system comprises: a pair of wheel displacing elements; fastening elements to releasably attach each wheel displacing element to the frame of the wheelchair through the openings; wheel holders for bearing respective rear wheels of the wheelchair, wherein each of the wheel holders is associated with a respective wheel displacing element, and the wheel holders define between them a shifted rear wheel axis; at least one anchoring link to releasably secure at least one of the wheel displacing elements to the frame of the wheelchair at an additional attachment point. Also provided are wheelchairs comprising such auxiliary frame system and methods to displace the position of rear wheels of a wheelchair.