If you use a serial protocol like Frame Relay which supports carrying multiple logical links on a physical link then connecting 38 client offices through your 3845 would be quite possible (if the serial link has sufficient capacity to aggregate the traffic from 38 client offices).
Or if you got a pair (1 would not be enough) of channelized serial links (like T3 or E3) and assigned a channel (or group of channels) to each client office it should be possible to connect 38 client offices through your 3845.
 I just did some checking and according to this link:
We are pleased to announce availability of Beta software for 16.6.3. 16.6.3 will be the second rebuild on the 16.6 release train targeted towards Catalyst 9500/9400/9300/3850/3650 switching platforms. We are looking for early feedback from custome...