I know of the following:
Davion - Liao (4th Succession War, Marik-Liao Offensive under SunTzu)
Davion - Steiner (FedCom Civil War)
Davion - Kurita (Kentares IV and aftermath)
Davion - Marik (part of Marik-Liao Offensive)
Any others?
Your question might be better answered by summarising all the inter-relationships of the Great Houses. We can start with the Federated Suns since they were for quite some time the protagonists of Battletech.
(1) Federated Suns
In general the FS borders hate their neighbours, the DC and CC, save for a time when Victor And Friends was a thing, with the notable exception of the CC who has NEVER gotten along with anybody and in fact backstabbed Victor the 1 time they pretended to. So the Capellan Confederation might be argued to be the biggest Great House enemy of the FS. All bets with the DC are now off however in the most recent timeline.
FS don't have as much a problem with the FWL save for the Joshua Marik Incident, and that was personal, and long past. This relationship bears watching in the current era... if the FWL can ever pull itself together long enough to forge one that is.
FS and LC, despite the Civil War, have a special relationship that has carried on to the Dark Ages. An old married couple comes to mind; they've squabbled, but they will stick together unless something REALLY bad happens.
(2) Capellan Confederation
They hate the FS, period. Take a look at the map and you'll know why.
The FWL are frenemies at best, waiting for mutual backstabbery at worst. Think US-(a certain ex-union) in the 90s... now extend the analogy to today. Mm-hmm, yeah.
The CC probably bear a grudge against the LC for their part in the 4th Succession War. Then again, they bear grudges against everybody. Even in the face of nuclear annihilation (Jihad) the CC won't play with nobody. Period.
The CC-DC thing never really got anywhere. See again CC, grudges, teamwork.
(3) Free Worlds League
If only because of the nuclear-fuelled hate-on between the FS and neighbours, the FWL-LC thing is on a
comparably low burn, but don't underestimate it: not only are they trade rivals worse than 2 ambitious VPs in an office with a dying CEO, a lot of territory on the border have changed hands and Hesperus is always there, always tempting the FWL.
FWL and DC probably do loads of trade. They probably talk a lot too. But a lack of mutual enemies and very different views on government, democracy, human rights, etc. precludes any real alliance.
(4) Lyran Commonwealth
Previous LC-DC fights have been interrupted by the presence of mutual Clan enemies. But they don't talk neither, and that silence speaks volumes. The LC's special relationship with the FS should preclude anything more concrete with the DC than silent, low-level trade.
(5) Draconis Combine
The DC's relationships with everybody have been covered, but a final postscript - where the CC is going into its own unique godlike-Great-Leader territory, and the FS considers themselves paragons of civilisation, and both the FWL and LC are in for the money, the DC traditionally considers itself the rightful heir to the Star League by dint of its leader being a sort of Vice-President after the Camerons at the time of the Star League's dissolution. Don't ask me how or why, it is what it is. So after the CC, it is the least likely to play nice with others.
Now throw in the Periphery States, minor Houses, special regions, those wacky Clans, etc...