does the rest of Gregor's family experince a metamorphosis as the story progesses?

Yes, the entire family experiences a metamorphosis of some type before the end of the novella. First, we have Grete, who after Gregor's metamorphosis attempted to take care of his every need. She tried to do for him, what he had done for the family. But over time, the care subsides, and she eventually comes to resent and despise him. 

Gregor's parents, also go through a type of metamorphosis but not as drastic. In the beginning they simply stop being themselves..... they stop talking, making noise, stop doing anything that they believe will bother Gregor. I believe they are repulsed but hopeful. His mother and father still have hope that he will return to himself and thing will go back to normal.

Gregor also finds that his parents weren't always what he believed them to be. This isn't exactly a metamorphosis, but rather a further revelation of how they took advantage of his help, misrepresenting their true circumstances. None-the-less, they eventually have to step up to the plate and actually work for themselves. They don't embrace it..... but they do what they have to do from necessity. A step forward?

In Chapter Three, having seriously injured Gregor, his father at last takes pity on him. Gregor's sister, who has been caring for him all along, and his mother, who clearly loves her son, had already taken the step towards accepting him which his father now undertakes. It is significant that the father is willing to accept the son only by crippling him in a display of his power. Now that his son has been subdued and thus seems to no longer pose a threat, he can be accepted as part of the family.

Prior to Gregor's death, the family also takes on three lodgers. But after his death, they tell them to leave bofre retiring to the country to regroup. Their is an optimism at this point in the story we haven't seen before.  decide that the future does not look bad as their jobs are all likely to lead to better ones and they will soon be able to find a new apartment that is smaller and easy to manage, unlike the one Gregor had picked for them. Mr. and Mrs. Samsa suddenly realize that their daughter has become very pretty and that it is time to look for a husband for her.