On the KKth best base of a matroid

Given a weighted matroid MM and a positive integer KK, the KKth best base of MM problem is to find KK distinct minimum (or maximum) bases regarding the weight function. This problem is NP-hard. We prove that it is polynomial for 2-sums of uniform matroids and a fixed number of kk-sums of series parallel graphs, M(K4)M(K4), W3W3, Q6Q6 and P6P6.