OK, here goes... Can a front derailleur triple , or for that matter a compact, be mated with an internal geared hub to increase gear choices? I've never seen it nor even discussed & I could use an experienced answer.

Yes, but you'll need some way to tension the chain. I've seen it done using a rear derailleur as a tensioner.

The literature that came with my Shimano Alfine IGH stuff had instructions for using two chainrings with the Alfine chain tensioner.

Please note that to use multiple chainrings you almost definitely have to have a tensioner capable of taking up more slack than the standard single-pulley tensioners. As mentioned above, a rear derailleur locked into place directly below the rear cog will probably work fine.

Yes, but it's not that simple.

First of all you'd need to use a derailleur chain, which isn't insurmountable since 3/32" sprockets exist for most, if not all, IGH hubs.

Now for the harder part, which may kill the deal. Since you're using different size sprockets you'll need a way to take up the chain slack on the smaller ones. They do make spring idler arms for this, so you can do what you propose, but you have to decide if the added complications are worth the expected benefit.

In my opinion, you should use either a derailleur system or an IGH hub. Using both together means having the drawbacks of both without fully realizing the benefits of either.

It's certainly doable, as long as the hub uses a sprocket that can accept 3/32" 'derailleur' chain, rather than the 1/8" thick 'single speed' chain as is commonly used on older IGH bikes. A rear derailleur fixed in one position (with either the limit screws or a short piece of cable) is needed to take up the slack. A two-pulley fixed tensioner will do the same job, but a low-end rear derailleur is far cheaper, especially as it's not being used to shift so quality doesn't matter as much.

The chainrings you should choose depends on what hub you're using. A 3-speed has widely spaced gears, so would benefit from 'half step' gearing. This is where the gears on one chainring fall exactly between the gears on the other. The idea here is that you'd use the hub gears to set the general range, with the front derailleur for fine-tuning. With a triple crankset, 'third step' gearing can be used with the same principle. Hubs with more gears would be better with a larger spacing between chainrings, giving two or three overlapping gear ranges as with a derailleur-equipped bike.

One thing to be careful of is over-torquing the hub. Sturmey-Archer 3-speeds seem to take whatever you throw at them, but other hubs have a maximum sprocket/chainring ratio which limits the low gear range you can get.

While to some extent, you get the drawbacks of both systems, you get some of the advantages too. The ability to shift at least some of the gears while stationary is an advantage when riding in traffic. A bicycle with vertical dropouts and an IGH must generally run a chain tensioner anyway, so substituting this for a rear derailleur is less of a disadvantage.

Instead of a FD, on my Brompton, I got a 2 speed planetary,
50-20t equivalent so wide 6 speed, but since both gears are planetary,

the double shifts 3<>4, can take place at any speed,
a good thing when bogged down on a hill..

Thanks for the informed replies, People. I've just gotten the education that I was looking for. GREAT HELP!