The description for Slow Fall is bare boned:
Beginning at 4th level, you can use your reaction when you fall to reduce any Falling damage you take by an amount equal to five times your monk level.
Essentially it functions as a level/feet dependent Feather Fall spell.
Unlike previous editions of D&D the 5th edition's version of Slow Fall doesn't require a monk to grab hold of nearby walls or trees to slow their fall: Essentially they drop like people in martial arts movies do. In our game it's considered a Ki ability that doesn't use Ki points and is described just looking cool.
Lacking any particular description shouldn't a monk be able to carry someone (a fellow PC clinging to their back, for instance) so long as the additional weight doesn't surpass the monk's encumbrance capacity?
If so then could a monk seek to catch someone who's falling and counter the fall with his/her allotted Slow Fall capacity so long as the encumbrance factor is respected?
In the first scenario if he carries a party member (say Lidda the Halfling from 3.5 edition) who is holding onto his back and doesn't overburden him then the two should land without problem.
In the second scenario Lidda has fallen and he jumps and catches her. The DM could rule that the monk's Slow Fall negates all damage but what she would take from the momentum (distance she fell) before she was caught or all damage period if it's within his allotted "damage reduction".