It is possible, but to be able to help first I need to know what this side menu is and is being called. How is the side of your site called? There is usually a file named sidebar.php
in the theme that is responsible for presenting information on the side, if this is the case you can use the is_*();
functions of WordPress to check which page is being accessed and call the correct menu, eg:
If you want a menu for home and another for all internal pages:
if( is_home() ){
// código do menu da home
}
else{
// código do menu das internas
}
If you want a menu for home, another for all internal, and a different one for the contact page, do the following:
if( is_home() ){
// código do menu da home
}
else if( is_page( 'contato' ) ){
// código do menu da página de contato
}
else{
// código do menu de todas as outras páginas
}
Notice that it's quite relative?