Possible rhymes with:
impossible, impossible, rosabelle, accessible, addressable, admissible, collapsible, compensable, comprehensible, crucible, defensible, dispensable, embraceable, enforceable, erasable, fixable, flexible, forcible, immiscible, impassable, impossible, inaccessible, inadmissible, incompressible, indefensible, indispensable, inexplicable, inflexible, insensible, invincible, irreplaceable, irrepressible, irresponsible, irreversible, leasable, miscible, nontaxable, noticeable, ostensible, passable, peaceable, permissible, reducible, replaceable, reprehensible, responsible, reversible, rosabelle, sensible, serviceable, taxable, traceable, unenforceable, unserviceable, untraceable
Possible sounds like:
passable, passably, passively, peaceable, peaceably, peaceful, peacefully, possibly, psychobabble