Basically, there is only one good way to enlarge an image in Photoshop, that is to say with image-> image-size, then to choose a good algorithm and possibly to try different ones, like described here.
The big problem with the logos is that many of them are quite small and if you try to enlarge them, they will always lose in quality and in breakage. You always lose quality when resizing.
According to my experience, this loss of quality can be reduced if you do not do it in one step but in several small ones and correct the image every time you see an error like the loss of quality. a clean edge. When you correct errors when the image is larger, you will need more work to make it look good.
For the most part, it's at least for me a track and a mistake and trying to get the best result.