A 52-year-old man presents with a 3-week history of progressive facial swelling over the left parotid region. On examination, there is a firm, non-tender mass palpable anterior to the sternocleidomastoid muscle. Intraoral examination reveals elevation and inward displacement of the soft palate. CT imaging shows a 4 cm heterogeneous mass within the parotid gland with involvement of the styloid process. What is the most appropriate next step in management?