The code is almost the same (see revised answer)... MAX plus 1 is now used for both INSERT statements because they are separate statements. Beware code like this, that it isn't accidentally rerun... either that, or add WHERE clauses to prevent problems if the NewComp rows already exist. Also understand that the SELECT part of an INSERT SELECT does not "see" any of the rows that the INSERT is inserting... I forget the technical word used to describe this behavior, but in the ancient language spoken by The People it is SQL-Anywhere-Does-Things-The-Way-They-Should-Be-Done.

"Helping with your homework" is something I can do, "doing your homework" is something you must do :)

First read this: http://dcx.sybase.com/1100/en/dbreference_en11/insert-statement.html

Then this MAY be a solution for you (it sorts existing NewCompN to the end):

insert into MaterialComponent 
on existing update 
select Material, 'NewComp1', 1+max(RowRn) 
  from MaterialComponent
 where Component not in ('NewComp1', 'NewComp2')
group by Material
;

insert into MaterialComponent 
on existing update 
select Material, 'NewComp2', 1+max(RowRn) 
  from MaterialComponent
 where Component <> 'NewComp2'
group by Material
;

commit
;

@Breck: Sorry, I know I must not do this, avoiding your attempt to bring this learner on the right path. But apparently a very strange variation of "Heartbleed" has attacked my mind so I coudn't resist. ;-)