In the present work, which aims at searching for bound sates, the interactions of the D-multi-ρ systems are investigated by means of the formalism of the fixed-center-approximation to Faddeev equations. Reproducing the states of f 2 (1270) and D 1 (2420) dynamically in the two-body ρρ and ρD interactions, respectively, as the clusters of the fixed center approximation, the state of D(3000) 0 is found as a molecule of D − f 2 or ρ − D 1 structures in the three-body interactions, where we determine its quantum number J P = 2 − and find another possible state of D 2 (3100) with isospin I = 3/2. In our results, there are some other predictions with uncertainties, a D 3 (3160) state with I(J P ) = 1 2 (3 + ) in the four-body interactions, a narrow D 4 (3730) state with I(J P ) = 1 2 (4 − ), a wide D 4 (3410) state of I(J P ) = 1 2 (4 − ), and another wide D 4 (3770) state but with I(J P ) = 3 2 (4 − ) in the five-body interactions, and a D 5 (3570) state with I(J P ) = 1 2 (5 + ) in the six-body interactions. Our results are consistent with the findings of quark models.PACS numbers: