Saxe Blue is a cool grey-green-blue, and the trick with any colour like this is to keep it from going cold and clinical. The fix is warmth — in the off-whites you pair it with, in the floor, and in the metalwork.
My honest recommendation: drench it. Walls and woodwork in the same Saxe Blue gives you that enveloping, atmospheric finish that this colour was made for. Stick a chalky white on the ceiling rather than carrying the blue all the way up. Paint & Paper Library Sand I (LRV 95.4) is gorgeous overhead — it reads as a soft warm white that takes the edge off the grey. All White from Farrow & Ball (LRV 92) is the cleaner option if you want the ceiling to recede crisply rather than warm things up.
Now the warmth. Saxe Blue needs a counterpoint or it sulks. Smoked oak floors and aged brass hardware are the classic move — that golden, slightly tarnished metal sings against cool blue-green. For accent colour, go earthy and rich. Mylands Cigar BH.20 (LRV 11.8) is a deep tobacco brown that's brilliant on a single feature — a door, joinery, even a piece of furniture. If you want something punchier, Dulux Copper Glow (LRV 30.1) brings an oxblood-meets-terracotta heat that lifts the whole scheme.
The "but what about" question I always get: can I add another blue or green? You can, but it muddies things — Saxe Blue is already doing the cool work. Better to let it be the cool note and lean hard into warm contrast everywhere else.
Practical tip: test the off-white on the ceiling before you commit. North-facing rooms will pull Saxe Blue greyer and colder, so the warmer Sand I will serve you better there. South-facing, you've got more latitude and All White will hold up fine. And don't skimp on the brass — cheap chrome will undo all the warmth you've worked for.