We studied asteroid clusters suggesting a possibility of at least two disruption events in their recent history ( \leq 5 Myr ) .
We searched for new members of known asteroid pairs and clusters and we verified their membership using backward orbital integrations .
We found four asteroid clusters , namely the clusters of ( 11842 ) Kap ’ bos , ( 14627 ) Emilkowalski , ( 63440 ) 2001 MD30 and ( 157123 ) 2004 NW5 that show at least two secondary separation events that occurred at significantly different times .
We considered a possible formation mechanism for these clusters : The parent of an asteroid cluster was spun up to its critical rotation frequency , underwent a rotation fission and was slowed down by escape of the newly formed secondary/ies .
Then the YORP effect spun up the primary again and it reached its critical rotation frequency and underwent another fission .
We created a simple model to test whether the scenario of two rotation fission events of a parent primary induced via the YORP effect is possible for the four clusters .
We obtained a good agreement between the model and the cluster properties for the clusters of Kap ’ bos and ( 63440 ) .
For the cluster of Emilkowalski , our model explained the unusually slow rotation of the primary .
However , the time needed for the primary to reach its critical frequency after the first fission event was predicted to be too long by a factor of several .
We suspect , considering also its D type taxonomic classification and the existence of a dust band associated with the cluster , that the asteroid Emilkowalski may actually be a cometary nucleus .
Regarding the cluster of ( 157123 ) , the final rotational frequency of the primary after the last fission event predicted by our model is in a good agreement with the observed rotation frequency of ( 157123 ) .
However , a separation of the older secondary is not possible in our model due to the deficiency of free energy needed for an escape of the large secondary .
This could be due to an error in the H value of the secondary or the possibility that we did not find the real primary of this cluster .