Is it possible to draw a line from the shield to the socket in an open way?

Good morning. I have a question. Prefabricated house with old aluminum wiring. The sockets begin to overheat and melt from the hair dryer, from the washing machine in the "Fast 30" mode. There is no possibility of gating walls and laying new wiring, since the apartment is rented. Is it possible by the rules to lay a new trunk from the shield, at least one or two outlets on concrete, without hiding the wires in the wall? Thank.