* Bank Coop, Migros Bank, Linth plan to co-operate with U.S.
* Up to 100 Swiss private banks expected to take up deal
ZURICH, Dec 11 (Reuters) - Three more Swiss banks said they would work with U.S. officials in a crackdown on wealthy Americans evading taxes through hidden offshore accounts, a trickle that could rise to about one third of the country's private banks.
The number that participate in the government-brokered scheme is important for larger banks facing criminal investigations in the United States, such as Credit Suisse , Julius Baer and Pictet & Cie.
These banks' talks with U.S. justice officials to settle their cases have been frozen pending a solution for the wider Swiss banking sector.
If the U.S. deems its deal with Switzerland a failure because too few banks come forward to make amends for aiding tax evasion, it is likely to hold up settlements for the larger banks.
The deal for second-tier banks, agreed in August, is part of a U.S. drive to lift the veil of Swiss bank secrecy which in 2009 led to UBS paying $780 million in a settlement where the bank agreed to hand over U.S. client names with secret Swiss accounts.
Bank Coop, Migros Bank, and Linth Bank said on Tuesday they would participate in the U.S. scheme.
They join Valiant Holding and Berner Kantonalbank , two mainly retail banks, that have also said they would take part. Zurich-based private bank and securities firm Vontobel Holding AG is also participating, but has put itself in a category of institutions that have not committed any U.S. tax-related offences and are therefore exempt from penalty payments.
Banks had until Monday to inform the Swiss regulator of their intentions.
Peter V. Kunz, professor of business law at Berne University, told Reuters on Tuesday he thought about 100 of the country's 300-plus private banks would participate.
The vast majority of Switzerland's private banks such as Geneva-based Lombard Odier & Cie are not listed on the stock market, meaning they are under no obligation to publicly disclose how they plan to deal with the U.S. tax crackdown.
Eleven listed banks, such as private banks EFG International and VP Bank and a host of small, largely retail players including local government-backed cantonal banks, have yet to tell shareholders what they intend to do.
The U.S. scheme, which lapses at the year-end, requires banks to hand over some previously hidden information and face penalties of up to 50 percent of assets they managed on behalf of wealthy Americans. If the banks shun the offer, individual firms and senior staff risk criminal prosecution.
Coop, majority-owned by Basler Kantonalbank which is among the banks in the crosshairs of U.S. prosecutors, said staying out of the programme was too risky.
Coop took a 9 million Swiss franc ($10.14 million) provision and said it had only a few customers who were based in the United States, whose assets amounted to less than 0.3 percent of its total.
Migros said it was coming forward following comments from the Swiss regulator, which told banks they should err on the side of caution in judging their dealings with American clients.
Linth said it is entering the program in an effort to bring the matter to a swift conclusion.