Routers by design are devices that have Layer 3 interfaces. They route traffic between different subnets connected to those interfaces. So implementing your topology, and requiring that multiple ports on the router be on the same subnet is defeating the purpose of the router. If you want everything on the same subnet, simply get rid of the router and connect the ASA directly to the switch.
Now having said that, there are situations where you would want to set up a router to function this way. This is a technology that goes by various names such as pseudowire, or xconnect, but officially, it uses what is known as Layer 2 Tunneling Protocol (L2TP). It essentially allows you to connect two or more hosts on the same subnet over a connection that consists of one or more routers. In a sense, it makes router ports function as switch ports. You can find out more about L2TP at the following lesson:
This is a feature that is supported only by certain routers, so you have to make sure that your platform and IOS allows it.
In addition, some lower end routers, such as the 800 series, have a built in switch. This means that four ports on that router actually function as a switch. So you can use those ports to achieve the topology you want.
You have to ask yourself, why do you want a router in there if you want only one subnet, if you don’t actually want routing capabilities and features? Ideally the ASA should connect directly to the switch in this case.
If however it’s absolutely necessary, the way to do it is using the L2TP protocol if your platform supports it.
I hope this has been helpful!