I would like to share my salary with a small group of family or friends. Is there a way to do this without the income being taxed twice (once for me and once for each friend?
Perhaps you could form a (non-profit?) corporation for this express purpose? It hires everyone in the group. The corporation then hires out its workers, bills for them and collects the money, and then distributes it to its employees according to whatever scheme is decided on. For instance, if you want to guarantee some minimum income to everyone, you can pay each person equally up to that amount, with additional funds being distributed according to whatever scheme you come up with.
Note that anybody in the group already employed would need to renegotiate their current employment through the new company unless they wanted to quit. The would include termination of most perks and benefits to be replaced with a somewhat higher compensation rate - basically becoming independent contractors through the new corporation. This is something everybody in the group would want to discuss informally with their employer ahead of time. I know some companies (especially smaller ones) that would have no problem retaining an employee by jumping through some hoops to contract them through an intermediary company but many other companies may have no defined process that would even allow them to do so and may not be willing to even consider it.
Of course you would want to consult with an attorney, accountant, etc. to determine if and how this would be set up and work out in your jurisdiction. For instance, the responsibility for certain taxes (FICA comes to mind in the U.S.) would fall on the new company.
I'm assuming US, but would vary by country/region.
If the disparity in income was low enough between members of this group, income could be distributed via gifts with no tax implications. For 2019 that's $15,000 per person, so one married couple could gift another married couple up to $60,000 with no gift tax or reporting requirement. There is no limit on the number of individuals they gift, so if one family has tremendous income, they might gift all other members of the community.
As far as formalizing/enforcing such an arrangement, doing so would change the nature of the money given (gifts can't be mandatory or given with expectation of reciprocity). A non-profit could be used to handle the distributions, but distributions from a non-profit aren't always considered tax-free gifts and likely this would not pass the charity tests to qualify the non-profit for tax deductible donations.
In some ways, employee-owned companies do this already, but typically those still have pay and ownership structures that value each employee at different rates. Paying all employees the same and sharing ownership equally would accomplish what you are suggesting financially.