ALTER PROCEDURE [dbo].[myProc]
AS
BEGIN
   SELECT * FROM myTable
END

SELECT * FROM myProc WHERE x = 'a'; -- But that doesn't work...

declare @as_condition varchar(500); --Your condition

create table #a
(
id bigint
)

insert into #a
execute sproc

declare @ls_sql varchar(max);
set @ls_sql = "select * from #a where " + @as_condition;
execute (@ls_sql);

ALTER PROCEDURE [dbo].[myProc]
    @X VARCHAR(10)
AS
BEGIN
SELECT * FROM myTable WHERE x=@X
END
GO

EXECUTE dbo.myProc 'a'

create table #sp_who (
  spid  	smallint,
  ecid  	smallint,
  status    nchar(30),
  loginame  nchar(128),
  hostname  nchar(128),
  blk   	char(5),
  dbname    nchar(128),
  cmd   	nchar(16),
  request   int)

insert into #sp_who execute sp_who

select * from #sp_who where spid < 10

ALTER PROCEDURE [dbo].[myProc]
@X VARCHAR(10)
AS

BEGIN
    SELECT * FROM myTable WHERE x=@X or @X = -1
END

GO

ALTER PROCEDURE [dbo].[myProc]