Is it permissible to transfer the remains of a father to a new grave, instead of leaving them in a grave that includes a large number of men and women, some of whom are strangers, and then his bones are collected later?

The burial method mentioned in the question contains several Shari'ah prohibitions: not digging, introducing a new deceased person into a grave with a previously buried one before the first has decomposed, and the mixing of men and women. The minimum for a grave is a pit that prevents odor and protects from wild animals. It is forbidden to introduce a new deceased person into a grave with another before the latter has completely decomposed; this determination should be made by those knowledgeable about the earth. The sanctity of a Muslim in death is like their sanctity in life, so it is not permissible to exhume their grave as long as their bones have not decomposed, unless they have decomposed and turned into dust, in which case it is permissible to exhume it or bury someone else in its place. It is not permissible to exhume a grave to move the deceased unless there is a legitimate Shari'ah purpose, such as separating the deceased from someone buried with them.