So that's what I was doing wrong

docs/pseudocode.txt

@@ -55,7 +55,7 @@ end
 
 TCP systems
 
-TCPNetworkManager:
+TCPNetworkManager: //NOPE
 	Init //opens the TCP server socket, and allocates the socket set
 	Quit //close the TCP server socket, and free the socket set
 	AcceptConnections //accept new connections

docs/server.txt

@@ -22,3 +22,10 @@ If a player is in motion, the server will update their internal position, but th
 
 This outline is only the most basic example of the server's operation possible, but it's a good start. I'll need to consider things such as server-specific map data, scripts and other resources being sent to new connections.
 
+-------------------------
+
+class Client:
+	ID --unique, incremental
+	socket --connection socket
+	[stuff]
+	[things]

server/tcp_network_manager.hpp

@@ -17,15 +17,15 @@ public:
 	int Send(int index, const void* data, int len);
 	int SendAll(const void* data, int len);
 
-	int OpenSocket(const char* host, int port);
+	int AddSocket(const char* host, int port);
 	TCPsocket GetSocket(int index);
 	int CloseSocket(int index);
 
 	int GetMaxConnections() const;
 	int GetCurrentConnections() const;
 private:
-	TCPsocket sock;
+	TCPsocket server;
-	SDLNet_SocketSet clientSocks;
+	SDLNet_SocketSet socketSet;
 };
 
 #endif