Amyloid fibrils are fibrillar deposits of denatured proteins associated with amyloidosis and are formed by a nucleation and growth mechanism. We revisited an alternative and classical view of amyloid fibrillation: amyloid fibrils are crystal-like precipitates of denatured proteins formed above solubility upon breaking supersaturation. Various additives accelerate and then inhibit amyloid fibrillation in a concentration-dependent manner, suggesting that the combined effects of stabilizing and destabilizing forces affect fibrillation. Heparin, a glycosaminoglycan and anticoagulant, is an accelerator of fibrillation for various amyloidogenic proteins. By using (2)-microglobulin, a protein responsible for dialysis-related amyloidosis, we herein examined the effects of various concentrations of heparin on fibrillation at pH 2. In contrast to previous studies that focused on accelerating effects, higher concentrations of heparin inhibited fibrillation, and this was accompanied by amorphous aggregation. The two-step effects of acceleration and inhibition were similar to those observed for various salts. The results indicate that the anion effects caused by sulfate groups are one of the dominant factors influencing heparin-dependent fibrillation, although the exact structures of fibrils and amorphous aggregates might differ between those formed by simple salts and matrix-forming heparin. We propose that a conformational phase diagram, accommodating crystal-like amyloid fibrils and glass-like amorphous aggregates, is important for understanding the effects of various additives.