The Positronic Man by Isaac Asimov & Robert Silverberg
In this book, by chance, a robot is manufactured that has more creativity and other human-like mental characteristics than other robots. It is explained that (with the manufacturing methods of that time) the pathways of a "positronic brain" were imprecise in the sense that no two were made exactly the same. Good fortune gave this robot ("Andrew") both an extraordinary brain, and also happened to place him in a home with a family that would be able to appreciate him and assist him.
After a period of time working as a household servant and becoming viewed as a part of the family by one of the daughters, Andrew carves a piece of wood for the girl. It turns out to be finely crafted. The family has him do more woodwork and it eventually evolves into a high quality wood craft / art business.
After some time, Andrew feels he would rather not be viewed by the law as a piece of property owned by the family - although he has no interest in leaving the family. With legal help, he wins the right to be considered a "free robot", but not a person or citizen.
This is the first step in a series of changes Andrew makes in the direction of being more human or human-like. Other steps include an android body with periodic upgrades to increase similarities to humans. Some of these may actually place limits on him, but give more in common with humans.
To pursue this course, Andrew designs / invents a number of artificial organs he intends to add to his body, but which can be adapted to humans in need of an organ replacement. Andrew becomes exceedingly rich and famous from his prosthetics business. Still, Andrew wants to be more human. And he wants to be legally accepted as a person. There is too much opposition to this among humans, who have various reasons for not wanting to accept a robot as an equal. Finally, Andrew believes he understands the main obstacle to human willingness to accept him.
The book does provide some opportunities to think about some issues. However, the book is more of a life story of an individual whose life raises questions. Even when it discusses the issues it does not explore that widely. For instance, there is never a mention of what might be reasonable criteria to determine whether a chimp, dolphin, other animal or an alien being deserved to be treated as a "person".
I would also suggest that while the character development may be enough for a book with a heavier emphasis on ideas, the characters are not as full as a reader of life story kinds of fiction may want.
I recently read Robert J. Sawyer's "Mindscan" which deals with some similar issues. Not only was Mindscan more idea-rich, but I found the characters more interesting. The Positronic Man is OK, but it could have been more.