We present a B-spline-based multichannel K-matrix method following an exten
sion from a B-spline-based configuration-interaction approach. Theoretical
procedures are presented in detail for its application to photoionization f
rom two-electron and divalent (e.g., alkaline-earth) atoms. Numerical examp
les, including doubly excited photoionization spectra above the N = 2 thres
hold from the He 1s2s S-1 metastable state, are also given.