Acidizing operations in subterranean formations that contain both a siliceous material and a source of calcium ions can often be problematic due to the generation of calcium-containing precipitates, particularly calcium fluoride. Methods for treating a subterranean formation can comprise: providing a treatment fluid having a pH ranging between about 1 and about 4.5 and comprising a chelating agent, hydrofluoric acid or a hydrofluoric acid-generating compound, and a compound having two or more quaternized amine groups; introducing the treatment fluid into a subterranean formation containing a siliceous material and a source of calcium ions; dissolving at least a portion of the siliceous material in the subterranean formation with the hydrofluoric acid or the hydrofluoric acid-generating compound; and complexing at least a portion of the calcium ions in the subterranean formation with the chelating agent.