You can just call the override method with super(), This could work for you:

class my_picking_extension(models.Model):
    _name = 'stock.picking'
    
    def onchange_picking_type(self, cr, uid, ids, picking_type_id, partner_id, context=None):
        values = super(my_picking_extension).onchange_picking_type(cr, uid, ids, picking_type_id, partner_id, context=context):
        #change the values
        values['value']['field_x'] = 'change value'
        return values

Here is the function I want to call. It is part of another model.

    def get_domain_for_onchange_partner_id(self, sale_or_picking_id):
        domain = {'carrier_id': [],
                  'delivery_service_id': []}
        if sale_or_picking_id.partner_id.id or sale_or_picking_id.carrier_id.id:
            result = self.get_delivery_option_default(sale_or_picking_id.carrier_id, sale_or_picking_id.partner_id)
            if result and result["level"]:
                default = result['delivery_option_default']
                # ignore carrier related default values when defaults come from a carrier itself
                if result["level"] != "carrier":
                    sale_or_picking_id.carrier_id = default.delivery_carrier_id
                    domain['carrier_id'].append(('id', 'in', default.allowed_carrier_ids.ids))
                domain['delivery_service_id'].append(('id', 'in', default.allowed_service_ids.ids))
                self.set_default_options(sale_or_picking_id, default)
        if sale_or_picking_id.carrier_id.id:
            domain['delivery_service_id'].append(('carrier_id', '=', sale_or_picking_id.carrier_id.id))
        return domain