  We consider a variant of the coded caching problem where users connect to two
types of caches, called private and access caches. The problem setting consists
of a server with a library of files and a set of access caches. Each user,
equipped with a private cache, connects to a distinct $r-$subset of the access
caches. The server populates both types of caches with files in uncoded format.
For this setting, we provide an achievable scheme and derive a lower bound on
the number of transmissions for this scheme. We also present a lower and upper
bound for the optimal worst-case rate under uncoded placement for this setting
using the rates of the Maddah-Ali--Niesen scheme for dedicated and
combinatorial multi-access coded caching settings, respectively. Further, we
derive a lower bound on the optimal worst-case rate for any general placement
policy using cut-set arguments. We also provide numerical plots comparing the
rate of the proposed achievability scheme with the above bounds, from which it
can be observed that the proposed scheme approaches the lower bound when the
amount of memory accessed by a user is large. Finally, we discuss the
optimality w.r.t worst-case rate when the system has four access caches.
