Alkali metal ions may lead to the production of insoluble materials during the course of stimulating a subterranean formation, particularly when acidizing a siliceous formation or a formation containing a siliceous material. Alkali metal ions may be sequestered using an alkali metal complexing agent in order to reduce their propensity toward forming insoluble materials in a subterranean formation. Methods for stimulating a subterranean formation can comprise: providing a treatment fluid that comprises an alkali metal complexing agent comprising a cyclic polyether having between 3 and 6 ether oxygen atoms present therein, and hydrofluoric acid, a hydrofluoric acid-generating compound, or any combination thereof; and introducing the treatment fluid into a subterranean formation.