We gave our daughter two middle names, mainly because we couldn’t agree on her first name! They are all family names (and also “royal” names!). We then faced the dilemma of doing that for the rest of our kids.... we didn’t, and they all only have one middle name. Funnily enough, her now partner also has two middle names, so they match!
There are quite a few instances throughout our families of two middle names.... my husbands grandfather, his sisters husband, their son, my niece, a grand-nephew and my new baby grand-niece! So two middle names isn’t strange to me at all.