Organisations had until the end of last week to submit expressions of interest to manage the services, which are being expanded from six to nine.
Some of the organisations, including the NCVO, Navca, the Charities Aid Foundation, Acevo and Volunteering England, are interested in submitting multiple bids, often as part of a consortium.
The NCVO wants to run seven of the nine services: collaboration; income generation; performance management; campaigning and advocacy; leadership and governance; responding to social change; and equalities and diversity. The equalities and diversity programme generated most interest.
"We believe we have expertise in these areas and we are bidding with partners, small and big, in all our bids," said an NCVO spokeswoman.
One partner is fellow umbrella group Navca, which is joining the NCVO for the first four categories listed above. Navca is also leading a rival bid with Charity Trustee Networks against the NCVO and others on leadership and governance.
Capacitybuilders - a non-departmental public body set up in April 2006 to improve the infrastructure of the voluntary sector - is due to publish its shortlist on 21 November, with a view to having programmes ready by next April. It confirmed there was no limit on the number of services an organisation could take part in.
Bill Freeman, director of development at Navca, said he thought more organisations would collaborate if they were not shortlisted.