We study transport through a quantum dot in the fractional quantum Hall regime with filling factors ν=2/3 and ν=5/2, weakly coupled to the leads. We account for both injection of electrons to or from the leads, and quasiparticle rearrangement processes between the edge and the bulk of the quantum dot. The presence of neutral modes introduces topological constraints that modify qualitatively the features of the Coulomb blockade (CB). The periodicity of CB peak spacings doubles and the ratio of spacing between adjacent peaks approaches (in the low temperature and large dot limit) a universal value: 2∶1 for ν=2/3 and 3∶1 for ν=5/2. The corresponding CB diamonds alternate their width in the direction of the bias voltage and allow for the determination of the neutral mode velocity, and of the topological numbers associated with it.