I have enlarged hundreds of negatives. My first step is to enlarge either the 35mm or the medium format onto a a 4x5 interpositive. To do this you need to make a very flat contrast negative. I use lith film in an old 4x5 film holder taped to the baseboard and do it right in the darkroom with safelights on. You should use red safelights, but I used with no problems yellow safelights. But just like paper you need to make a test strip of the interpositive to see what times give you the density you are looking for. I do not have a densitometer, so I go by look. I will post the pic of a contact 4x5 test strip in the non photo gallery. The development of the film is done in the regular chemistry I use for making prints. I also found that to get the flattest, nicest interpositives, nearly exhausted developer works best. I process for 1 minute. But this is not a hard and fast rule. Sometimes it takes a bit more time, sometimes a bit less. The nice thing with the safe ligths, is you can watch it develop. Once I have established the correct time for the interpositive, I then do the full sized interpositive. What is fun about that is you get to see the film look like it would if it were a picture. It shows you all the flaws and such. From there I make an 8x10 negative using the lith film processed the same way. But instead of a full sized test strip, I cut the film down into three pieces to make the test strip. The 8x10 negative needs to be of a high contrast. The exact opposite of the interpositive. I can also at this stage if I stop the lens down, I can add time to the exposure and if need be do a bit of minor burning or dodging. I will also post a interpositive in the non picture gallery.
This is just my steps in making an enlarged negative. I didn't put in any of the things I do to make the image flat or such.