Of the 46 per cent of members who responded to the consultation, which asked if independent providers should become fully integrated members, 75 per cent voted in favour.
The proposal for inclusion will now be put to a vote at the organisation's annual general meeting in June.
The confederation is proposing to 'amend the definition of its core membership so it is open to any organisation delivering frontline services in England'.
If accepted, voluntary and not-for-profit organisations as well as private sector providers will become full members of the confederation.
At present such providers are only allowed to represent their views alongside core members when there is a 'shared agenda'.
Confederation chair Peter Mount said: 'By expanding our core membership we will continue to reflect the modern NHS.'
A confederation spokeswoman added that discussions about establishing a network for independent providers within the organisation, assuming they were admitted as core members, were 'ongoing'.
She added that the issue was discussed at all membership meetings and several specific focus groups, and that the level of support for the proposals matched the results of the vote.