Getting Links in Multiple Categories (intersection)

I am using get_bookmarks() to get bookmark links. I can get links posted in cat A or cat B, but I only want links in both A and B.

Example what I need:

I have three link categories cat#1, cat#2, cat#3.

I need to get links in both cat#1 AND cat#2 not cat#1 OR cat#2 (intersection).

I am currently using:

$links = get_bookmarks(array('category' => $term_ids));

Which doesn’t work because of how get_bookmarks() works.

        $category_query = '';
        $join = '';
        if ( !empty($category) ) {
                $incategories = preg_split('/[\s,]+/',$category);
                if ( count($incategories) ) {
                        foreach ( $incategories as $incat ) {
                                if (empty($category_query))
                                        $category_query = ' AND ( tt.term_id = ' . intval($incat) . ' ';
                                else
                                        $category_query .= ' OR tt.term_id = ' . intval($incat) . ' ';
                        }
                }
        }

^{Note from the Editor: Adding sample code for easier understanding – Bookmarks get queried with an OR clause by default. As they’re retrieved via $wpdb->get_result(), there’s no easy solution in filtering aside from the queried result.}

Any help or idea of different approach would be much appreciated.

UPDATE

I am trying to make a new function out of get_bookmarks() function.

I changed the code that shown above to this below (changed OR to AND). But now nothing is returning. Perhaps i need to change the SQL to something else. So, I will need advice on this.

if ( !empty($category) ) {
        $incategories = preg_split('/[\s,]+/',$category);
        if ( count($incategories) ) {
            foreach ( $incategories as $incat ) {
                if (empty($category_query))
                    $category_query = ' AND ( tt.term_id = ' . intval($incat) . ' ';
                else{
                    // sisir
                    $category_query .= ' AND tt.term_id = ' . intval($incat) . ' ';
                }
            }
        }
    }

It should be as simple as that: Just get the terms from the link_category and use the get_terms() argument instead, which should work like you need it.

get_terms(
     'link_category'
    ,array(
         'include'      => array( 1, 2, 3 )
        ,'orderby'      => 'name'
        ,'order'        => 'ASC'
        ,'hierarchical' => 0
     )
);