Mega Menu Walker

If I understand the problem setup correctly, you could try to do the break and widget class counting within the wp_nav_menu_objects filter.

Here’s an updated example, it’s rather expanded because of the extra debug part:

add_filter( 'wp_nav_menu_objects', 
    function( $items, $args  ) {

        // Only apply this for the 'primary' menu:    
        if( 'primary' !== $args->theme_location ) 
            return $items;

        // Here "x_" means the latest root li (depth 0)
        static $x_pid           = 0;      // post ID of the latest root li (depth 0) 
        static $x_key           = 0;      // array key of the latest root li (depth 0)
        static $x_cols          = 0;      // n breaks or widgets gives n+1 columns  
        static $x_has_dropdown  = false;  // if the latest root li (depth 0) has dropdown

        // Internals:
        $tmp            = array();  
        $debug_string   = '';
        $show_debug     = true;  // Edit this to your needs:

        foreach( $items as $key => $item )
        {
            // Debug:
            $debug                              = array();
            $debug['ID']                        = $item->ID;
            $debug['title']                     = $item->title;
            $debug['key']                       = $key;
            $debug['x_key']                     = $x_key;
            $debug['depth']                     = '';
            $debug['menu_item_parent']          = $item->menu_item_parent;
            $debug['has_widget_class']          = 0;
            $debug['is_depth_1_first_child']    = 0;
            $debug['x_has_dropdown']            = 0;
            $debug['has_break_class']           = 0;
            $debug['x_cols_increase']           = 0;

            // Collect columns increaments:
            $inc = 0;

            // Depth 0:
            if( 0 == $item->menu_item_parent )
            {
                $debug['depth'] = 0;

                // Resets:
                $x_key          = $key;
                $x_pid          = $item->ID;                            
                $x_cols         = 0;
                $x_has_dropdown = false;

                // If widget class exists:
                if( in_array( 'widget', $item->classes, 1 ) )
                {
                    $debug['has_widget_class'] = '1';
                    $inc++; 
                }       
            }

            // Depth 1:
            if( $x_pid == $item->menu_item_parent )
            {   
                $debug['depth'] = 1;

                // Increase the columns count for an existing dropdown:
                if( ! $x_has_dropdown )
                {
                    $inc++;
                    $x_has_dropdown = true;
                }

                // Check for the 'break' class: 
                if( in_array( 'break', $item->classes, 1 ) )
                {
                    $debug['x_has_break_class'] = 1;

                    // First li child:
                    if( $x_key+1 == $key+0 )
                    {
                        $debug['is_depth_1_first_child'] = 1;
                    }
                    else
                    {
                        $debug['is_depth_1_first_child'] = 0;
                        $inc++; 
                    }
                }

                $t[$x_key] = $x_cols;
            }           

            $debug['x_has_dropdown'] = (int) $x_has_dropdown;

            // Increase the columns count:
            $debug['x_cols_increase'] = $inc;           
            $x_cols += $inc;
            $debug['x_cols'] = $x_cols;

            // Collect the debug:
            $debug_string .= print_r( $debug, 1 );
        } // end foreach

        // Show debug info:
        if( $show_debug ) 
            printf( "<!-- debug: %s -->", $debug_string );

        // Insert the new 'mega menu' class to the corresponding menu object:
        foreach( $t as $key => $value )
        {
            $items[$key]->classes[] = sprintf( 'mega-menu-columns-%d', $value );
        }

        return $items;

    }
, PHP_INT_MAX, 2 );

With your current menu tree, I get this debug information:

<!-- debug: Array
(
    [ID] => 3316
    Mega Menu Walker => About Us
    [key] => 1
    [x_key] => 0
    [depth] => 0
    [menu_item_parent] => 0
    [has_widget_class] => 1
    [is_depth_1_first_child] => 0
    [x_has_dropdown] => 0
    [has_break_class] => 0
    [x_cols_increase] => 1
    [x_cols] => 1
)
Array
(
    [ID] => 3317
    Mega Menu Walker => Company Profile
    [key] => 2
    [x_key] => 1
    [depth] => 1
    [menu_item_parent] => 3316
    [has_widget_class] => 0
    [is_depth_1_first_child] => 1
    [x_has_dropdown] => 1
    [has_break_class] => 0
    [x_cols_increase] => 1
    [x_has_break_class] => 1
    [x_cols] => 2
)
Array
(
    [ID] => 3318
    Mega Menu Walker => Our Team
    [key] => 3
    [x_key] => 1
    [depth] => 
    [menu_item_parent] => 3317
    [has_widget_class] => 0
    [is_depth_1_first_child] => 0
    [x_has_dropdown] => 1
    [has_break_class] => 0
    [x_cols_increase] => 0
    [x_cols] => 2
)
Array
(
    [ID] => 3319
    Mega Menu Walker => Leadership Team
    [key] => 4
    [x_key] => 1
    [depth] => 1
    [menu_item_parent] => 3316
    [has_widget_class] => 0
    [is_depth_1_first_child] => 0
    [x_has_dropdown] => 1
    [has_break_class] => 0
    [x_cols_increase] => 0
    [x_cols] => 2
)
Array
(
    [ID] => 3320
    Mega Menu Walker => Professional Affiliations
    [key] => 5
    [x_key] => 1
    [depth] => 1
    [menu_item_parent] => 3316
    [has_widget_class] => 0
    [is_depth_1_first_child] => 0
    [x_has_dropdown] => 1
    [has_break_class] => 0
    [x_cols_increase] => 0
    [x_cols] => 2
)
Array
(
    [ID] => 3321
    Mega Menu Walker => Clients
    [key] => 6
    [x_key] => 1
    [depth] => 1
    [menu_item_parent] => 3316
    [has_widget_class] => 0
    [is_depth_1_first_child] => 0
    [x_has_dropdown] => 1
    [has_break_class] => 0
    [x_cols_increase] => 1
    [x_has_break_class] => 1
    [x_cols] => 3
)
Array
(
    [ID] => 3322
    Mega Menu Walker => Partnerships
    [key] => 7
    [x_key] => 1
    [depth] => 1
    [menu_item_parent] => 3316
    [has_widget_class] => 0
    [is_depth_1_first_child] => 0
    [x_has_dropdown] => 1
    [has_break_class] => 0
    [x_cols_increase] => 0
    [x_cols] => 3
)
 -->

If you want to check if the walker object is of the megaMenuWalker class, you can use:

if( ! is_object( $args->walker ) || ! is_a( $args->walker, 'megaMenuWalker' ) )
    return $items;

instead of

if( 'primary' !== $args->theme_location ) 
            return $items;

I hope this helps.

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