As House lawmakers prepare to take up budget amendments that would force the city to keep open all 26 libraries, Boston Public Library officials are circulating a memo saying that could lead to more layoffs.

One of the amendments reduces state support by $2.4 million if all the branches aren't kept open. Four branches are currently slated for closure, including the Lower Mills library, following a vote by library trustees earlier this month.

The House is expected to debate amendments affecting the library system today.

In the memo, library officials say the system will see 31 additional job cuts if the amendments are approved. The borrowing of books from other libraries for BPL users would stop, they add.

There would also be:

-- A reduction in the purchase of new books, such as novels, travel guides, atlases, how-to books, best sellers and award winning titles, CDs, DVDs for the Central Library and branches

-- Commercially-licensed databases and highly popular digital downloadable books, music, and video used throughout the state by students of all ages, the business community, and the general public, are likely to be further reduced and limited in use

-- Possible ending of digitization efforts, which have made more than 20,000 historical titles of interest to students, genealogists, and historians accessible via the internet

The full two-page memo is attached.