When you take a spur off a socket, the spur load does not pass through the socket. The connection is in the terminals. In one wire and out the other.In my opinion the potential issue ( Although not in your case ) with adding two spur cables from a ring final circuits socket ,and connecting double sockets to each spur cable ,is the donor sockets ability to cope with the combined potential loads. If I recall correctly most are rated 16 to 20 amps.
Would be interested to know others opinions.