All I can say is my sister has a great dane and it does wonderful sorry but just about all dogs. seh has chihuahuas, pomeranians, sorry schnauzer, cockers, Jack Russels.

Great Danes tend to plop down on things and could hurt a small dog. From my experience they are also fairly low energy dogs. I would suggest something really solid and equally mellow like a bulldog. The breeds you mention would likely annoy the Dane to no end.

Chihauhau’s,Dachshund’s, and Jack Russel terrier’s would be good they arent usually timid dogs so they wouldn’t be as fearful of the Great Danes size.

Personally I would go with a mini Ratt terrier.
they are a high energy tough little dog that I think would do very well with a Great Dane.
I know that they do very well with larger breeds.
they are a very sturdy dog and they are able to keep up with a larger high energy dog.
Also unlike the smaller dogs that you have named they are not delicately structured and another big plus they have no known health problems.
Many Ratt owners also own Pitt Bull, Rotts,or Mastiffs.
If you are thinking of a good little dog to go with yours this is the best breed that I could think of. There are breeders listed on line please go and check them out.
Good luck with finding another dog.

pugs we had 4 Doberman and we brought the pugs home now they think they are the size of Doberman lol they play and treat the Doberman like they are litter mates and the Doberman do the same .

My Great Dane Lucy gets along with all small breed dogs but for some reason really likes pugs. She is always very curious about pugs and spend a lot of time sniffing and the like

A miniature schnauzer. They are very smart.