  In the literature, most of the known high-rate $(n,k)$ MDS array codes with
the optimal repair property only support a single repair degree (i.e., the
number of helper nodes contacted during a repair process) $d$, where $k\le d\le
n-1$. However, in practical storage systems, the number of available nodes
changes frequently. Thus, it is preferred to construct $(n,k)$ MDS array codes
with multiple repair degrees and the optimal repair property for all nodes. To
the best of our knowledge, only two MDS array codes have such properties in the
literature, which were proposed by Ye and Barg (IEEE Trans. Inform. Theory,
63(10), 2001-2014, 2017). However, their sub-packetization levels are
relatively large. In this paper, we present a generic construction method that
can convert some MDS array codes with a single repair degree into the ones with
multiple repair degrees and optimal repair property for a set of nodes, while
the repair efficiency/degrees of the remaining nodes can be kept. As an
application of the generic construction method, an explicit construction of
high-rate MDS array code with multiple repair degrees and the optimal access
property for all nodes is obtained over a small finite field. Especially, the
sub-packetization level is much smaller than that of the two codes proposed by
Ye and Barg concerning the same parameters $n$ and $k$.
