My husband and I moved from the Chicago area with 5 cats and 1 very large dog. We used a pet transport service Starwood Pet Relocation. I was extremely OCD, and my contact was extremely patient. They provide a relocation person to load the pets on the plane in Chicago, another in Frankfurt to unload them and walk them through customs and return them to the onward flight. A third person was in Lisbon to offload them and walk them through Portuguese customs.
Two kitties travelled in the passenger cabin, and three travelled with the dog in travel appropriate travel containers. We flew from Chicago to Frankfurt, where the pets were carried from the plane to the excellent airport pet veterinary hospital to be let out of their kennels and into pet kennels for feeding watering, exams and leg stretching. We were sent pictures of them both before they were boarded in Chicago and while they were at the pet hospital. The regulations require that there be a stopover for us since the timing of our onward flight to Lisbon precluded a quicker transfer. That was Ok since it gave all of us the chance to decompress overnight. The next morning, we got on the plane to Lisbon and the baggage handlers and the relocation folks let us know that all critters were safe and sound. The longest phase was them having to wait in their kennels in Lisbon customs for 6 hours. They arrived with us at our destination residence and were thrilled to be out of their kennels; litter boxes and dinner were ready, and they slept soundly.
The paperwork has to be completed by the US vet at the last minute, so that can be a nail biter.
We asked the TSA folks to let us go to a private room to scan the kitties that travelled with us on the passenger cabin. I didn't want to drug the animals. Please let me know if you have other questions. Vicki