insert trigger to auto-set key fields for composite primary key

Basically the next step for https://dba.stackexchange.com/q/330357/272354 : I created a trigger after insert to set SEQ to the highest SEQ plus one if it's less than one. Basically: ~~~lang-sqlite3 CREATE TRIGGER TRG_NAMES_ADD2 AFTER INSERT ON NAMES FOR EACH ROW WHEN NEW.SEQ < 1 BEGIN UPDATE NAMES SET SEQ = (SELECT IFNULL(MAX(SEQ), 0) + 1 FROM NAMES WHERE TYPE = NEW.TYPE) WHERE TYPE = NEW.TYPE AND SEQ = NEW.SEQ; END; ~~~ However I'd like to do the same thing for TYPE independently from SEQ. The problems I found were that I can have only one UPDATE per trigger, and the AFTER INSERT triggers may be executed in any order. I tried a second trigger like this: ~~~lang-sqlite3 CREATE TRIGGER TRG_NAMES_ADD1 AFTER INSERT ON NAMES FOR EACH ROW WHEN NEW.TYPE < 1 BEGIN UPDATE NAMES SET TYPE = (SELECT IFNULL(MAX(TYPE), 0) + 1 FROM NAMES), SEQ = 1 WHERE TYPE = NEW.TYPE AND SEQ = NEW.SEQ; END; ~~~ However for completeness TRG_NAMES_ADD2 should run after TRG_NAMES_ADD1, or I would have to put both actions (set TYPE to a possibly new value (if < 1), and then use that new value to possibly set a new value for SEQ (if < 1), too) into one trigger. Unfortunately that's beyond my capabilities. For convenience, here's the table creation and some sample inserts: ~~~lang-sqlite3 CREATE TABLE NAMES ( TYPE INTEGER NOT NULL, SEQ INTEGER NOT NULL, NAME VARCHAR(20), PRIMARY KEY (TYPE, SEQ) ); insert into NAMES (type, seq, name) values (2, 3, "T1"); insert into NAMES (type, seq, name) values (2, 0, "T2"); insert into NAMES (type, seq, name) values (2, 0, "T3"); insert into NAMES (type, seq, name) values (0, 1, "T4"); insert into NAMES (type, seq, name) values (0, 0, "T5"); ~~~ So the assignments should be like this: ~~~lang-text T|S|N ----- 2|3|T1 # T,S set manually 2|4|T2 # S set automatically 2|5|T3 # S set automatically 3|1|T4 # T set automatically 4|1|T5 # T,S set automatically ~~~