Wiktionary
coming on to
vb. (present participle of come on to English)
Usage examples of "coming on to".
Who did he think he was, coming on to her in such a crude way when he had a-well, a virtual slave at home, one who was pregnant with his child?
She arrived in Cairo this morning and will be coming on to Luxor shortly.
Their way lay west, and if Tell were alive, he would be coming on to join them if by some chance he was not already there before them.
Sean saw the barrels of the cannon swing slightly, coming on to aim.