another possible BASH way - create a helper function which process the stdin with `read` command and then prints extra line(s):

 $ function append_lines(){ local data; while read -r data; do echo -en "$data"; done; echo "$*"; }
 $ echo "`date `" | append_lines " +suffice line1" " ++line2" " +++line 3"
 Mon Aug 21 15:55:01 CEST 2023 +suffice line1 ++line2 +++line 3

where 
- `while read -r data; do echo -en "$data"; done;` - just passes pipe through
- `echo "$*";` - prints all arguments of append_lines()