Functionality

So capitalism doesn't work.

This is pretty easy to demonstrate; we're in the middle of a mass extinction caused by capitalistic forms of social organization.  Present expectation is that the mass extinction is going to include us.  (The Involuntary Human Extinction Project has succeeded.)

Even theoretically, it's easy to demonstrate; capitalism seeks to increase profit. Value is the ratio of benefit to cost.  To increase profit, you need to either lower benefit or increase cost.  So capitalism is a mechanism to destroy value.  (As we do indeed see happening all over the place as the social barriers to treating profit as a goal, rather than a measure, collapse.)

Socialism also doesn't work.

This is a bit harder to demonstrate; you can start in on the linear optimization problem of a command economy, but someone can quite correctly point out that socialism doesn't necessarily imply a command economy.

The easiest way to grasp this (I think) is that any system has stocks, flows, feedback, and constraints.  (The mythological market is supposed to provide feedback, for example, in capitalist systems.)  The problem with socialism -- anything where you're taking "according to ability/according to need" or collective ownership of the means of production seriously -- is that you wind up with scale-invariant constraints.  That won't work.  It wouldn't work even if you could get the Angel of the Lord to quietly remove all the greedheads.

Consider -- In Soviet Russia, how many socks you are issued and when they are laundered (and where they are laundered...) is decided in Moscow.  You live in eastern Siberia and you herd horses.  This is very very bad; when you have socks, they neither fit nor have been washed.  In Soviet Russia, national emissions and atmospheric dumping policy is decided in Moscow.  That's pretty good, or at least it could be; that's the correct scale of collective to be addressing that problem.  The scale of the decision must be appropriate to the scale of the problem to have an effective solution. (And if you've got an intractable deadlock the issue is pretty much that you need to change the scale of the mechanism that's looking at the problem.)

Mixed economy?  It doesn't stay mixed, because the rich win the argument about the economy is for.

You can have something that exists to guarantee, defend, and extend existing wealth, or you can have something that exists to create a general prosperity.  You can't have both.  (The objectives are opposed!  "both?" is a bit like saying "hot AND cold".)

So what do you do?

No rich people.  If you want the general prosperity version, there have to be hard income and asset caps, and they have to be relatively low; around an order of magnitude more than the lower of the mean/median income as the income cap, for example.  (50 kCAD/annum median income, 500 kCAD/annum is the income cap.  The PM's salary is set a x8; I'd cap CEO salaries there, too.)

The limited liability corporation functions, effectively, as "you can't complain when I steal this".  Don't have those.  (Collectives, partnerships, and other forms of collective organization already work pretty well.  They'd work better if they were in an regulatory and legal environment where they were normalized rather than opposed.)

There's a really intractable fact that the solution has to be as complicated as the problem.  Social organization that forbids collective responses to problems is equivalent to an assertion that the problem must not be solved.  (Not that it can't be solved; that you're not allowed to solve it.)

So ... experiment.  Consider the possibilities of really full service credit unions.  (Housing is a way for capital to make everyone pay them to live.  The fix is to make housing something that's collectively arranged and managed.  And then you can diversify the investments, and start running a daycare, and then start buying things collectively.)

While you're experimenting, recognize that the purpose of the legal system is NOT to provide feedback; it's to set constraints.  ("Work or starve" is feedback.  "Everybody eats" is a constraint, at least if you attach legal liability to political units when that isn't factual there.  You need to pick your constraints carefully because lots of people prefer murdering the poor to providing them food.)

Also recognize that land is alive, and you make rules for it as though it is alive, and not dead.  (E.g., you own a Picasso.  (A painting by the famous painter of that name.)  You really own it; no liens, it's not loan collateral, you've got simple clear title.  You throw it through a wood chipper.  You have probably upset many people but you have not done wrong.  But throw a dog through a woodchipper and you have done wrong; the relative prices of the Picasso and the dog are not what's relevant, it's the categories.  The painting is dead and the dog is alive.  Pave over grassland and you have also done wrong.)

This is not actually difficult to do, it's giving up on the possibility of being king that's challenging.  (You can have success, or control.  (That is, be king; everybody has to do what you say.)  Trying for control precludes success.)