your current 'sproc' is:
select column1,column2,column3,column4
from TABLE
where columnID in (SELECT Val from dbo.fn_String_To_Table(@MultiVal,',',1))
you could make another stored procedure identical to 'sproc' but add insert into TABLE (column1,column2,column3,column4) to the query.
insert into TABLE2 (column1,column2,column3,column4)
select column1,column2,column3,column4
from TABLE
where columnID in (SELECT Val from dbo.fn_String_To_Table(@MultiVal,',',1))