There is Berkeley DB/SQL (now sadly owned by Oracle), which is essentially Sqlite with BDB instead it's original B-tree implementation, that supports multiple parallel writers. Also Firebird can be used as in-process embedded database and supports multiple writers (in fact in the server mode it uses same file-locking based synchronisation mechanisms as in embedded mode)
On the other hand it is somewhat rare to see aplication that really needs multiple writers and would not be better served by full fledged database server.
Berkley DB is not as reliable as SQLite. Subversion, before switching to own storage, where known for data corruption problems attributed to Berkley DB.
I remember the old days when people would refer to berkdb as "Berserkley" because it tended to go berserk on your data. It's always had a bad reputation for reliability.
On the other hand it is somewhat rare to see aplication that really needs multiple writers and would not be better served by full fledged database server.