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A quantum superintegrable system is an integrable n-dimensional Hamiltonian system with potential: H=Delta_n+V that admits 2n-1 algebraically independent partial differential operators commuting with the Hamiltonian,the maximum number possible.The system is of order L if the maximum order of the symmetry operators is L.Typically,the algebra generated by the symmetry operators and their commutators has been proven to close polynomally for n<3 and for systems of order L=2 for general n.However the degenerate 3-parameter potential for the 3D extended Kepler-Coulomb system (2nd order superintegrable) appeared to be an exception as Kalnins et al.(2007) showed that it didnt close polynomially.The 3D 4-parameter potential for the extended Kepler-Coulomb system is not even 2nd order superintegrable.However,Verrier and Evans (2008) showed it was 4th order superintegrable,Tanoudis and Daskaloyannis (2011) showed it closed polynomially.We consider an infinite class of quantum extended Kepler-Coulomb systems that we show to be superintegrable of arbitrarily high order and explain the (apparent) anomalies of these systems.A main conclusion is that rational,nonpolynomial closure,is the expected result for higher order superintegrable systems in n> 2 variables; polynomial closure is very special.Joint work with Ernest Kalnins and Jonathan Kress.