Rib Cage Muscles
External intercostals (Ext IC):Posterior in general, running downward and forward from the rib above to the rib below.

Internal intercostals (Int IC):Anterior in general, running downward and backward from the rib above to the rib below.

Parasternal intercostals (PS IC):Anterior, specifically intercartilaginous continuation of the internal intercostals - running downward and backward from above to below.

Function of the intercostals:Classically the Ext IC ÷ inspiratory and Int IC ÷ expiratory. However, PS IC are ÷ inspiratory, and all IC's become expiratory at high lung volumes. Intercostals muscles may have more of a role in stabilizing intercostal spaces and ribs and maintaining posture than overall movement of the rib cage.
Scaleni C4 - C8
From transverse process of C3, C4, C5, C6, and C7.

To: anterior and medial aspects of the first rib and posterior aspect of the second rib.

Function: to elevate the rib cage.
Sternocleidomastoid CN XI
From: Sternum and medial clavicle

To: Mastoid and occipital process.

Function: elevate the rib cage.