When using Darkrai & Cresselia LEGEND's "Moon's Invite" attack, can you move damage counters to/from more than one Pokemon?
Yes. Basically the attack let's you rearrange your opponent's damage counters any way you want, as long as other effects, Poke-POWERs, Poke-BODYs, etc. will allow.
Source: Triumphant FAQ (2010-11-04), PUI Rules Team (2010-11-04)

Relevant cards

Note: All applicable cards may not be listed below.
HGSS4_100
HGSS4_99