Step-1 Install multi_search module.
Step-2 inherit = 'product.product' class in .py(Python file) in multi_search module.
In below example, I have custmozied .py file. You can directly copy the below python code in multi_search module -

 

class product_product_override_search(osv.osv):
    ''' Override search function
    ''' 
    _name='product.product'
    _inherit = 'product.product'
new_args = []
        for search_item in args:
            if len(search_item) == 3 and search_item[0] == 'name':
                multi_search = search_item[2].split(split_element)
                if multi_search > 1:
                    total_split = len(multi_search)
                    for i in range(0, total_split):
                        if i != total_split - 1:
                            new_args.append("&")
                        new_args.append(('name', 'ilike', multi_search[i])) 

                else:
                    new_args.append(search_item)
            else:
                new_args.append(search_item)
        return  super(product_product_override_search, self).search(cr, user, new_args, offset, limit, order, context, count)