Considering that you're reporting you're wired at 10A/circuit, I'm assuming you're outside the US and on 220/240. I'm not saying they don't exist, but a 10A residential circuit in the US would be most unusual where most are 15A for a normal 120V circuit(and I have 20A in my garage at home, which is not uncommon).
It's literally been years since I unplugged my 6890, but it's the single most power hungry device in the system, especially if you're running an aggressive temperature ramp. This is true of GCs in general, not the 6890 specifically. The ovens are incredibly well insulated, but a typical HP/Agilent sized dual column oven(I don't think the basic oven size/design has changed a ton since 5890 even though the everything around it has) still takes a lot of power when you start hitting 40º/min ramps especially when the temperature is already high. In the US, HP/Agilent GCs, or at least 5890/6890s wired for 120(which everyone I've ever used has been), actually specify 20A and every one I've used has a 20A plug on the cord. Not that the specifics matter for someone outside the US, but if you look at a normal 15A US plug(NEMA 5-15P), facing toward you orienting the ground pin up, the two power blades are parallel to each other and perpendicular to the ground. On a 20A 120 plug(NEMA 5-20P), such as a 6890 will normally have, the left blade(again facing plug, ground pin up) will be rotated 120º, left blade parallel to the ground and perpendicular to the other blade. BTW, the NEMA 5-20R will have the right slot(facing the receptacle) "T" shaped to accept both a 5-15 and 5-20 plug.
Of course 20A on 120 translates roughly to 10A on 220/240V, so you can half these numbers above.
Again, US installation, but I have run a complete GC-MS system-GC, MS, pump, and computer off a single 20A quad outlet box. Mine(6890, 5973) would be on one now if I didn't need two additional outlets for the G1512A ALS controller(not needed on later 6890s that use the 7863 series ALS with the controller integrated into the GC), the ion gauge, and had the rough pump plugged into its own outlet(common practice you'll find discussed here-I don't think Agilent endorsed officially other than for diagnostics, but something the independent/former HP/Agilent trained FSE I use recommends and something necessary if you use a larger pump than what the 5973 shipped with). If you count, that's 7 plugs total(GC, MS, pump, ALS controller, gauge, computer, monitor). I also at one point, at a previous job, had a 5890, 5971, Varian DS102 pump, G1512A, ion gauge, and seldom-used 5890 FID/NPD(No MS) on one circuit. Both GCs ran off the same computer, a Pentium 4 era Dell. That brings us to 9 separate plugs. I finally had to relocate the second 5890, as even though it was seldom used, having the 5890/5971 system sit at idle along with the pump would bring things down. That got interesting, as it needed to be where it was both for gas plumbing and for HPIB reasons(I don't know what the limitation HPIB length is, but it's sure a lot more difficult to run an HPIB cable to the other side of the lab than it is a LAN cable, and I really didn't want to have to set up a second HPIB system). I think I bought a bit of time by shifting to vac pump to a separate circuit, which freed a few amps and also made sure even if the breaker running everything else tripped I'd keep low vac running.
To get down to the point with your question-let's look at individual power requirements:
Looking at a photo I have handy of an eMod for a 5897 first gen(HPIB), input is specified at 900VA, with 400VA out for the pump. I would assume a 5973N isn't much different. That leaves 500VA for the MS itself, which is ~2.3A on 220. I'll treat the pump separately in a minute, as your life might be easier to power it separately.
The 6890 is the wildcard in this, as the 220/240V version came in both a fast oven and slow oven version. I'll go out on a limb and say 99% of US ones are 120V, which is only slow oven, so that's my familiarity. The site prep guide says that Denmark and Switzerland were the only countries fitted with "slow" 230V ovens. I'm not an electrician and I'm not going to pretend to offer an answer, but if I had to guess if you operated the oven as if it were a slow oven, you MIGHT be able to keep current draw under 10A. I've never stuck a Kill-A-Watt on a GC to see what idle, isothermal, etc power draws are. Holding at 50º or so, 250º inlet, 250º transfer line should hold you under 10A I would expect. If you are doing isothermal runs or modest temperature programs-I don't recall fast vs. slow oven specs, but rule off thumb offhand without really digging would be 40º/min max under 150º, 20º/min max above there you are probably okay. What could be an issue is if you are doing a higher temp isothermal run and just plug in 200º or whatever and let it do its thing-in that case I'd probably use a 20º/min or so method to get the oven close to there before loading the isothermal method. I'd check, double check, and triple check my circuit breaker on that circuit to make sure it's actually tripping properly(and might be tempted to throw a Kill-a-watt on the GC to monitor actual current). Whatever the case, have the GC on its own circuit, separate from everything else.
Everything else is probably fine on its own circuit. If you're using an E2M1.5 pump, it should be fine plugged into the MS, even though again that's not preference. The motor specs on that pump are nice gentle 1.2-1.3A when running(on 200-230V), but start-up is always a big deal on any kind of electric motor like this. Startup on 200-230 is 5.1-5.3A, though(depending on 50 vs. 60hz)-yet another reason why I like running these separate. Those of us in the US get to see 11.2A start-up on 60hz at 120 with this pump(the Varian DS102 I love is a full 42A start-up on 120V 60hz...).
Still, though, through a lot of rambling I'll say that a normal 220V spec 6890 on a 10A circuit might make me nervous...and BTW I pull those numbers from the site set-up guide for a stand-alone 6890.
