welcome.
I guess everyones got to start somewhere even if it is a small experiment.
If you truly wanted just to raise the karat and if you have hallmarked gold, proof them on a touchstone maybe instead of going through the time and cost of the GR process and simply add a few grams of 9999 gold bullion shot, or buy a maplegram or something simmilar even just a damaged 9999 gold coin with nothing but its intrinsic bullion value.
Charts for karating gold alloys are easy to find. Oppi Untracht Metal Techniqes etc
If you are invested into the Gold refining process the guys here like Frugal etc will not steer you wrong, research ALOT, use the search function, get your procedure clear in your mind as to what you want to do, but do not overcomplicate it.
In your position if i wanted to raise the Karat of the alloy from a refining perspective and a first foray into gold refining without going in heavy, i would go simply to a inquartation and use that as a first experiment but your gold will not be clean like when you buy 9999 shot for a new scratch alloy of a given Karat.
Whatever you decide you will always get sound advice from the senior guys experienced in the art of refining, of which i am not one.
If you melt use the right torch and fuel, i do not recommend OXY Acet at all for gold, oxy LPG will get the job done, i use the MECO midget as its also handy for platinum welding, as far as Oxidation is concerned, its inevitable with once cast Karat alloys, so a borax lined melt dish is your friend there, but there will almost always be junk if you are not making Karat alloys from scratch with pure silver, gold, copper etc. Having a history in the jewelry trade this sort of thing is fairly unavoidale with working already cast gold alloys, thats why we always add an amount of new pure metal, especially when forming or casting, as Frugal said the oxides can play hell with your plans, i only get one chance as i make one off designs for wax mold investment casting, sometimes it takes a week just to finsh one, no cadcam wax for me, so porosity is something i am well versed with from once cast metals.
If you are the do it yourself type, there is much info on the tube regarding making your own furnace, some good and some terrible, i used a large LPG cylinder and made one in a front loading format as i did not want to double handle a hot crucible and need to switch tongs, i go stright to pour, also i never need to melt more than 1 kg at a time, my furnace will easily do it, i just do need that capacity, so mine is LPG/Air burner you can even find some very good and efficient and well made stainless burners fabricated and sold on ebay as i did, not just bunged together plumbing pipe fittings.
From memory furnace i made was related to a tube regarding blacksmithing, was an aussie vid too, i just adapted it to what i wanted.
Heres a few pics of my, its around 6 yrs old now, i have never had any issues, and it totally made at home except the burner. and is excellently insulated with high temp thick Zircon Ceramic fibre wool, sealed and lined in a product called RTZ washcoat made here in my capital city with a sliced with a hacksaw Bubbled Alumina brick for a floor. A few pics incase you wanted to get the gist of what i am rambling on about.
And no i do not use my furnce mounted on a plastic milk crate, its up off the floor as its winter here and the concrete holds alot of moisture, this little guy will easily melt 1Kg+ of silver and beyond, and get yourself the required PPE, reflective aramid gloves etc, dont forget your eyes, you do not want to be looking into a white hot furnace without protection. IMHO DO NOT USE LEATHER, once hot and heatsoaked they BURN.
