Q:

How to add several partners to the project.project model?

I need to have more then one partner of a project in project form. Thats what I've tried:
class project(models.Model):
    _inherit = 'project.project'
    partner_id = fields.Many2many('res.partner',
        string='Customer',
        default=_get_default_partner)

Install failed with error "unknown function _get_default_partner". Allthrough the function exists in inherited model project.project.
The second version makes no change. After isttallation I went to Settings > database > modules > project > project.project and saw the partner_id is still many2one:
class project(models.Model):
    _inherit = 'project.project'
    partner_id = fields.Many2many('res.partner',
        string='Customer')

A:

You can use a lambda function to assign the default value like this:
partner_id = fields.Char(
    string='Customer',
    default=lambda self: self._get_default_partner(),
)

@api.model
def _get_default_partner(self):

    # override the original method

Actually, you should create another different many2many field. Instead of trying to convert the many2one to a many2many field. So I would do something like this:
class ProjectProject(models.Model):
    _inherit = 'project.project'

    partner_id = fields.Many2one(
        invisible=True
    )

    partner_ids = fields.Many2many(
        string='Customer',
        comodel_name='res.partner',
        default=lambda self: self._get_default_partner_ids(),
    )

    @api.model
    def _get_default_partner_ids(self):

        # [...]

