Two suggestions come to mind.

I've found that a Rimowa Notebook case has enormous room inside, specifically the LH model. The prime benefit is that case is designed to slide over the carry-on luggage case handle, and move as one unit together, easily, and quickly.

Prior to that I used an aluminum Rimowa Topas case, combined with a slim, minimalist black leather doctor's or barrister/lawyer's attache for decades. I looked in Spain, Italy, Germany, Austria, GB, and in North America, and finally found exactly what I wanted in a custom leather store at the Iguatemi Shopping Centre, in Fortaleza, Brasil.

I was flying back to Europe, and decided to do some shopping on the way to the airport. Looking at a leather belt, I glanced over and saw exactly what I wanted nearby. At those prices then I purchased both. Well crafted, two snaps, and elegant black leather. It has always looked good, constantly received compliments, and I could hold the attache handle atop the Topas, pulling both along easily as one unit without effort.

The two were a good combination for weekends, or an "extended" business week when I missed flights, and sometimes had to stay overnight ( Business always comes first ). Today, even with somewhat tight carry-on restrictions on LH or SR, the two combined have not created problems regarding last minute cargo bay storage requests at the boarding gate.

Conversely, the combination of an alu Topas carry-on case and an alu attache case have been flagged at the gate and even once while checking luggage at the LH counter at LAX to FRA. The excuse was the flight was too crowded, and the fact that the luggage was all LH models did nothing to impress the humour-less LH staff behind the ticket desk.