Can I handle multiple client requests of different action types with one action server?

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I have a requirement as follows:

One GUI window has an Action Server. This should serve multiple client requests (may be one at a time) but each request type is different (ex:- 1.MoveAction 2.RunAction 3.WalkAction) Based on the request, the message type will be different. The Action server should be able to recognize it in executeCB and serve the request back. (just like a web server) Is that possible with action lib?

I could write all the messages in one combined custom message and set an indicator for request type but that takes so much memory for each request that i make. I think there should a better way to do it.

Please let me know if you need any further information. Thanks in advance.......

Edit 1: Method overloading is not an option... Cuz action server definition is as follows with the message type:

actionlib::SimpleActionServer<aps_msgs::FileSelectAction> as_;

Can we make the initialization of the action server more generic?