No, but you can use components to this effect. Here is a common idiom that I use:

public with sharing class standardControllerExt {
  public ApexPages.StandardController standardController { get; set; }
  public standardControllerExt(ApexPages.StandardController controller) {
    this.standardController = controller;
  }
}

<apex:page standardController="Account" extensions="standardControllerExt">
  <c:commonComponent standardController="{!standardController}"/>
</apex:page>

<apex:component selfClosing="true" controller="commonComponentController">
  <apex:param name="standardController" required="true" description="The standard controller to use." type="ApexPages.StandardController" assignTo="{!standardContrller}"/>
</apex:component>

public with sharing class commonComponentController {
  boolean init;
  apexpages.standardcontroller controller;
  public commonComponentController() {
    init = false;
    // do NOT initialize anything that depends on "controller" here
  }
  public void setStandardController(ApexPages.StandardController con) {
    if(init) {
      return;
    }
    this.controller = con;
    // do more initialization here.
  }

  public ApexPages.StandardController getStandardController() {
    return controller; // Required for component to be happy.
  }
}

For example, we have this massive program we're about to release (ERP, here we come!) that uses "line items" in many different places (more than eight). We use one common component that is called by each page, resulting in very minimal duplicated code. The trick is how to initialize this setup correctly; follow this starting point, you should do okay.