Can we used multiple controllers on a single visualforce page ?

You can't directly reference the other classes (extensions) in the same page, but you can make variables static, assuming they participate in the form; this requirement exists because static variables are transient (do not serialize into the view state). A simple example follows:

Page:

<apex:page standardController="Account" extensions="ext1,ext2">
<apex:form >
    <apex:inputText value="{!message}"/>
    <apex:outputText value="{!ext1message}"/>
</apex:form>
</apex:page>

Ext1:

public with sharing class ext1 {
    public static string message { get; set; }

    public ext1(ApexPages.StandardController controller) {

    }
}

Ext2:

public with sharing class ext2 {

public ext2(ApexPages.StandardController controller) {

}

public string getext1message() {
    return ext1.message;
}
}

When you type a message and press Enter, it will be echoed back from ext2's getExt1Message() function. As you can see, you can use static variables. The caveat is that message is bound to a form element and will be submitted each time the page posts. Without the apex:inputText element, this code wouldn't work.

Since your comments specify that it is a boolean value that is calculated, you should probably store the results of the value into an apex:inputHidden element so that the form will correctly pass the value between extensions.