Don't change the soil level on your plants by adding compost all the time. I would mulch it with something to keep the weeds down. I'm not familiar with bio-intensive. Just plain old gardening and a little involved in permaculture.

Steve Moore is a well known biointensive high tunnel grower with many details on web. Also Eliot Coleman's book on winter gardening has many details on maintaining soil life for year 'round production. Neither of these are HI climate zones, but they are particular about adding a thin layer of compost before replanting their beds. Harvey Usery has also published comments about too much compost and how to remedy this. As time passes, you will learn to 'read' your soil/crops.

Your specific microclimate (temp, rainfall,light,wind) and crop choices will also determine your soil's on going maintenance needs. Of course, annual soil assessments via ag extension may be useful.

Enjoy your garden. Biointensive is addictive!

I plant intensively in raised beds.

After harvest I mix in a bit of compost and it mixes in my dried grass clipping mulch as well. If a heavy feeding crop I add commercial granular fertilizer like Dr. Earth or Whitney Farms according to recommendations on the box or bag. Smooth out soil & replant that same day.

Helpful to shade new transplants esp. in your warm climate. Be creative with rigging shade for them -- an inserted piece of cedar shake, upturned cardboard box or plastic rubbermaid tote (propped up a bit with bamboo stakes for air circulation). After a day or so plants will be fine without the shade. Greens especially will take off if you've not disturbed the roots much and have provide shade & water.

To maintain intensively planted bed -
put back in what you take out in the form of compost + fertilizer.

If minerals are in short supply in your soils you'll have to add some of that, too. Here we add lime yearly in the form of calcium carbonate. Rains 9 months of year wash it all away.

Should find info from the master gardeners in Hawaii about your soils and how to maintain them for gardening. Adapt their recommendations to your methods esp. organic.

Hope that helps,
Corrine

Here is a link that might be useful: Hawaii master gardener program

Corrine, do you soil test your garden? From what I've been told in master gardening, you shouldn't add lime without doing so.

I'm not too familiar with Hawaii climate, but many of your leafy greens, especially the kales & lettuces may do better as cool-season crops. Collards tolerate the heat a bit better.

But you might want to look into some perennial subtropical stuff as well. Malabar spinach, okinawa spinach, new zealand spinach, chayote squash... And don't forget moringa oleifera!

Everyone loves their familiar temperate vegetables, but some of the sub-tropical and tropical stuff is really tasty and lot easier because you don't have to mess around with sowing seed, double digging and transplanting every couple of months. Biointensive is great, and I have some double-dug beds, but I love my perennials.

Eh, Dan,
I've used this in both New Zealand and Hawaii year round--in raised beds or terraced beds--cheating a bit, cuz I rarely dug after the first double dig. I just put well aged compost on top and plant straight into it, and loosen the soil if I have to a bit with a fork. (If you're in a wet windward area, your soil may be too heavy to be able to get away with that...)

I grow a lot of greens, and interplant soybeans to add nitrogen (ainaola seed has a variety called 'green local'). Manoa lettuce works great, and you can put it along the edges of your beds of taller plants--I use a slightly smaller in-bed spacing than in the charts for that, about 6 inches.

Biointensive is great for small spaces. Just make sure you put back in what the plants take out, and rotate so that you're not planting the same kind of plant that you just harvested. Good compost is really the key. In the early 80s I found a great plan for a 3-bin composter that has served me very well in 'Crockett's Victory Garden'--a spin-off from a WGBH show on PBS. That was a long time ago but it's still around...here's a link to a site I just found with the same plans:
Good luck!

Here is a link that might be useful: Compost Bin Plans