firm something up
1. Lit. to make something more stable or firm. We need to firm this table up. It is very wobbly. You need to use a whisk to firm up the egg whites.
2. Fig. to make a monetary offer for something more appealing and attractive and therefore more "solid" and likely to be accepted. You will have to firm the offer up with cash today, if you really want the house. Please firm up this offer if you still want the house.
firm up
1. Lit. to develop better muscle tone; to become less flabby. I need to do some exercises so I can firm up. You really ought to firm up.
2. Fig. to become more stable or viable; to recover from or stop a decline. The economy will probably firm up soon. I hope that cattle prices firm up next spring.