We explore whether KamLAND and solar data may end up inconsistent when analyzed in terms of neutrino oscillations. If this turned out to be the case, one would be led to conclude that there is more new physics, besides neutrino masses and mixing, in the leptonic sector. On the other hand, given that KamLAND and solar data currently agree when analyzed in terms of two-flavor neutrino oscillations, one is able to place nontrivial bounds on several manifestations of new physics. In particular, we compute how well a combined KamLAND and solar data analysis is able to constrain a specific form of violation of CPT invariance by placing a very stringent upper bound on vertical bar Delta m(2)-Delta(m) over bar (2)vertical bar < 1.1 x 10(-4) eV(2) at the three sigma confidence level (m refers to neutrinos, (m) over bar to antineutrinos). We also estimate upper bounds on sin(2)theta -sin(2)(theta) over bar. These are quite poor due to the fact that matter effects are almost irrelevant at KamLAND, which leads to an intrinsic inability to distinguish whether the antineutrino mixing angle is on the light ((theta) over bar < pi/4) or dark side of the parameter space ((theta) over bar > pi/4). We briefly discuss whether this ambiguity can be resolved by future long-baseline (v) over bar (e) <-> (v) over bar (e,mu) searches.