The Immigration Department of Malaysia does grant in-country extensions to the Short Term Social Visit Pass, generally for a 30-day period. To make a request, you'd have to visit the Kuala Lumpur Immigration Department headquarters.
It has to be done in person, and you'll need your passport, any supporting documents, confirmed ticket home (or visa and ticket to third country), and to complete Form IMM.55. Extensions are meant to be granted for extenuating circumstances (illness, accident, conflict in home country), although visitors may be given additional time for less urgent reasons. A visa run to Singapore is an alternative, but does not guarantee readmission at the border.
While Travelfish.org author Pat Fama described how to accomplish both, the article is dated 2012. More recent feedback elsewhere and on this very site suggest that it is no longer as easy as it once was.