There are a couple different aspects to the electrical system upgrades. As I recall it, originally the brown wire mod pertained to increasing the wire/cable capacity from the battery to the main input power on the fuse box. That could be done either way; add a second wire of about the same gage to double it, or replace the original wire with a much heavier one. Either way works the same. Since you will be replacing the fuse box, I'd be inclined to just replace the wire to make a cleaner install.
Anther common electrical upgrade that is sometimes also referred to as the brown wire mod has to do mostly with the ignition (key) switch. It handles a lot of load as most of the electrical system passes the power through it. In order to lower that load relays are added to the major power consumers (can be any or all of several things). I believe this is the type of upgrade that
@ricar is referring to. With the addition of a relay you need a "trigger" wire and a power or "load" wire. The trigger wire can be the original wire that supplied the component you are supplementing with a relay. Then add a second heavier load wire to actually feed the power to that component. That is what he is saying.
While you are improving the electrical system, also consider a couple more items. The cable between the alternator and the starter isn't as heavy as it should be. Replace that with a regular "battery cable" sized cable. Some also like to replace the cable from the battery to the starter. The original one isn't that small so this is not absolutely essential.
Electrical grounds are a common problem throughout the vehicle. Personally I like to improve them by making more secure and positive connections to the chassis and replace all of the ground connectors to "ring" terminals (so they can be screwed down rather that the push-on type). Along with this you may also want to add a heavier ground strap between the engine and chassis. That can be by adding a second one rather than replacing it.
These will all take some time and effort to do, so be patient and diligent at it....you'll get there.