Winter Squash Spacing

I am gearing up to grow squash at my yarden.
I have 3 beds filled with excellent soil, each is roughly 4'x4' and a foot deep.
There is plenty of room for the foliage to run rampant across the landscape.
What kind of spacing would make sense in this situation?

I have two more 4'x4' beds that are filled 3' deep with autum leaves.
I have lots of rich compost, so I was thinking I could add zai pits in the leaves, but again, how many plants fit in this space?

We have eight 4x4 beds close to the house. I would put one squash plant in each corner of a bed and plant other stuff in the middle, hoping to encourage the vining squash to spread away from the beds. I find that bush-forming squash like zucchini take up 9/16 or even the entirety of those beds, but you can plant quick stuff like lettuce and radish around them.

Something that worked out rather well for me was utilizing cattle panel trellis for winter squash.

I bent a cattle panel fence into a U between two 4x12 beds so you could walk underneath it past the beds. Bent it was almost six foot tall at the apex. It originally was for cucumbers that did wonderful on it. Suddenly, I had butternut vines start growing and succession fruit after the cucumbers were finishing up. Left me a ton of ground space and minimized the space the vine's actually took up so I could grow other things.

I do the same as Christopher- I have limited "good dirt" space and a lot of 'not-so-great' dirt space, so I put the squash in a corner and encourage it to run wherever the dirt is not so great, so the space in the middle can be used for other stuff.
The squash will also climb, generally, so if I have old passionfruit trellises I try to encourage it to go up there too.

Thanks for the replies!

The spaces in between the beds is about 3 feet.
I could put an arch over those spaces, but I don't want to limit access for tending the beds.
I suppose I will be wading through the any foilage that spreads into the path, which might limit access to the bed as well.

Each of these beds is against a solid wood fence , and I have lots of bits of mesh fence to hang as trellises, so that is definitely happening.

I don't have any mesh fencing that could be self supporting as an arch, but I do have plenty of wood.
No need to build an arch, persay, any shape that bridges the space will do.

Each of these options is more work, but I love building infrastructure, so I don't consider that to be a bad thing.

For infill crops, would long term crops with taller growth be viable?
I'm thinking sunflowers ,corn, or even fruit tree cuttings.

Squash vines seem to grow through (and climb) corn just fine at my place. I grow beans on sunflower, but haven't done squash with them. People commonly report that sunflower is allelopathic...it hasn't seemed like a problem for me, but it could be.

i also let them run among my corn. Sunflowers are generally a winter thing for me, while squash is spring/summer, so not sure.
i think a lot will depend on your site, weather, and specific squash issues (bugs, mildew vs sun/ventilation). I cut off a lot of squash leaves when they start getting moldy, and at that point try to keep them growing up off the ground or away from the other plants i don't want mildew on.

I've had some weed trouble in the spaces between the 4x4 beds.
Poison ivy in particular.
Before building up an over those spaces I am thinking I might want to digout those spaces and fill them in with leaf mould slow compost.
I can walk on compost, and even plant into it, and the squash can grow on and over it.
Committing to woodchip pathways every where is more than I can handle, but I can tackle one 3x4 spot at a time.
I'll need to move a yellowhorn tree that's been languishing for years, but that's for the best.
I think I'll plant it right into one of the raised beds.

I've found it depends somewhat on the variety you want to grow.  I've had some winter squash / pumpkins that are very vigorous and will grow quite a long distance while others are much much content to take up less space.  Growing up is a great idea, but that would be better for squash that don't get too terribly large, otherwise you'll be worried about supporting the fruit.  (Think acorn squash versus a massive Hubbard squash as example.)  I'd also consider what the area is like for sun / water / air flow.  

From my experience, I'd think 4' is a bit tight for planting multiple plants, but one can certainly get away with it if one isn't interested in anything else being visible come late summer.

Also of note is that this family of plants will root at leaf nodes along the vine,  so if it has access to ramble, the plant can work on obtaining water and nutrients, although it would have more difficulty getting through lawn grass or a significant mulch layer.

Good luck.

Variety is gonna kind of a crap shoot.
My wife saved a huge  amount of seeds from grocery store spaghetti squash, and asked me to grow them out.
Obviously there's no telling what they crossed with and how they will turn out.

I don't mind the resulting chaos, I love her enthusiasm!
She wants low carb storage foods, like squash and onions, and I am happy to oblige if I can.
Last season I basically left this yarden of mine fallow.
Squash running rampant all over the yard will be almost ideal.

Thinking more about infill plants, corn will be too greedy/ needy, but tree cuttings/seedlings should be OK.
My wife wants some staghorn sumac, so maybe some of those, plus whatever else is handy.
Beans could also fit in pretty well, I think, preferably something that is best in its dried form.

She wants low carb storage foods, like squash and onions, and I am happy to oblige if I can.

 Garlic could go in the center now though many plant it in fall.  onions should be compatible but need  more to have vines kept away to prevent shading because they do not get as tall.

I love my cattle panel arches & used them for butternut squash, delicata squash, pumpkins & grapes. The airflow & sun around the plants keeps them healthy & easier to deal w those nasty, nasty squash borers! But they do need to be trained to climb. Mostly they prefer to crawl along the ground where they can secure themselves to the ground with roots along the vines.
This year I’ll be rotating out the squashes & growing cantaloupe, watermelon & cucumbers on the arches.
Some people put twinkle lights on their cattle panel arches for a sparkly summertime garden delight!

Here’s a photo of one of my arches

My own experience replanting onion bottoms has convinced me to try it as my primary means of propagation, so any losses to squash shouldn't be a big deal.
Planting garlic in the dead of winter is very appealing.
The beds have deep mulch on top.
I've seen onions  grow right through this, but they were full bulbs, taken from dumpsters and replanted.

I plant squash at the edges of the garden and let them run out over the lawn. Neither the squash nor the lawn grass appear to take any harm. I also use squash as a ground cover in my corn. Only problem is to move the vines away from the corn stalks so it doesn't pull them down. Works best if the corn is wide-spaced, or you won't get much squash.

The wintersown squash are coming up!

I planted 4 tubs of squash starts.
One came up fully, two not at all and the 4th has a sing big healthy start.
I will be planting some out, under a bell, since we are not at last frost yet.

Do you plan on transplanting individual squash plant or putting the whole tub of seedlings in the bed? The squashes already have 3-4 true leaves each I am afraid the roots are quite developed to be separated.

There are way too many to put in one bed.
I'll tease them apart and take my chances.

I just planted the other tubs with corn and beans, and I used pots, mostly 4".

Plants in the cucurbit family don't like root disturbance, so they may be set back quite a bit (pouting time) after having roots teased apart.  In the future, you may want to use some smaller pots for starting two or three seeds of winter squash.

That reminds me...it's probably about time for me to get mine started...just got back Sunday from two weeks away.