It's possible to use InnoDB with UNA, it's functioning better in hight concurrency, but some server side tuning is needed to avoid deadlocks. 

First set (or add) the following line into inc/header.inc.php 

define('BX_DATABASE_ENGINE', 'INNODB'); ///< db engine

after 

define('BX_DATABASE_NAME', 'xxxxxx'); ///< db name

Then the following server side settings for MySQL is needed in [mysqld] section:

innodb_stats_on_metadata = off
innodb_buffer_pool_instances = 4 # number of CPUs
innodb_buffer_pool_size = 4096M # ~80% of available RAM

transaction_isolation = READ-COMMITTED # or tx_isolation = READ-COMMITTED
lock_wait_timeout = 4
innodb_lock_wait_timeout = 4
innodb_rollback_on_timeout = 1
binlog_format = MIXED
innodb_log_file_size = 400M

#innodb