A few behemoths are increasingly dominating the municipal market, helping to lower prices for many investors but also sparking worries about concentration and influence.

There has been a mammoth shift in the $4tn muni market over the past decade as investors have increasingly used professional money managers to invest in both high- and low-grade state and local government debt. Mutual-fund holdings of municipal bonds now total $738.6bn, according to Federal Reserve data, a more than 50% increase since 2009.