Implement Custom FormsAuthenticationModule and replace the default

I cannot find any information on how to implement custom FormsAuthenticationModule.

Specifically, I want to implement a MyFormsAuthentication that mirrors most features ofFormsAuthenticationModule, or child of FormsAuthenticationModule

<httpModules>
  ...<add name="FormsAuthentication"
       type="System.Web.Security.FormsAuthenticationModule" />
  ...</httpModules>

MyFormsAuthentication can be used by the element in web.config, instead of the default FormsAuthenticationModule:

<authentication mode="Forms" />

The reason is that I want to support the domains format below:

Set A

a.domain.com

a.x.domain.com

a.y.domain.com

Can share cookie within set A.

Set B

b.domain.com

b.x.domain.com

b.y.domain.com

Can share cookie within set B.

Cookies (including Forms Authentication cookie) cannot be shared between domains of set A and set B, but use the same code base.

Current implemention

FormsAuthenticationTicket is used to generate forms auth cookie.

Any idea, or better solution?

https://msdn.microsoft.com/en-us/library/aa480476.aspx