Hi Enrons,
Welcome to the BuddyDev forum.

To answer your question, let us inspect the edit template. If you open the yourtheme/members/single/profile/edit.php ( or buddypress/members/single/profile/edit.php ), you will see at the top a line, something like this

if ( bp_has_profile( 'profile_group_id=' . bp_get_current_profile_group_id() ) ) :
	while ( bp_profile_groups() ) : bp_the_profile_group(); ?>

bp_has_profile() function is responsible for building the loop. Note that bp_has_profile is passing the ‘profile_group_id’ as argument.

The function

bp_get_current_profile_group_id()

returns specific group id(if you are viewing edit profile group, e.g. example.com/members/yourname/profile/edit/group/2/ will return 2), in all other cases, the function returns 1.

So, if you are not on edit profile group, the function always returns 1. 1 is the ID of base profile group, that’s why it is always showing base profile group.

Note:-
Please do not use

bp_get_template_part( 'members/single/profile/edit/group/4')

That line assumes you have a file named 4.php in your members/single/profile/edit/group/ folder in your theme( I don’t think that was your intention ).

Now, let us talk about the solutions to your issue:-

Method 1:-

Filter on ‘bp_get_current_profile_group_id’ like this

add_filter('bp_get_current_profile_group_id', 'my_profile_group_id');

function my_profile_group_id( $profile_group_id ) {

if( $somecondition & this is my page ) {//replace this line with your condition
$profile_group_id = 3;//or any other group id

}

return $profile_group_id;
}

Or Method 2:-

Filter on ‘bp_before_has_profile_parse_args’ or ‘bp_after_has_profile_parse_args’ and modify the group. I prefer the 2nd hook as it gives parsed arguments.

Example:-

add_filter( 'bp_after_has_profile_parse_args', 'buddydev_modify_profile_edit_loop' );

function buddydev_modify_profile_edit_loop( $args ) {

	//check if it is not our page, just return the args
	if( ! $my_page ) { //modify it for the condition

		return $args;
	}

	//it is our page, modify the values
	$args['profile_group_id'] = 3;//change the profile group id

	//you can change the following fields too
	//possible fields are
	//$args['user_id'] = bp_loggedin_user_id();// ,
	//$args['hide_empty_groups'] = true;// hide empty group?
	//$args['hide_empty_fields'] = false;
	//$args['exclude_groups']    = '1,3';//change it, It is comma separated list of profile groups ids to exclude
	//$args['exclude_fields']   = '';// // Comma-separated list of profile field IDs to exclude
	
	return $args;
}

I have listed all the interesting options it provides and you can uncomment and use any of those to modify the loop

Method 3:-

I will personally prefer it as it is much simple.

Make a copy of yourtheme/members/single/profile/edit.php, include it wherever you want. Just make sure to modify the line

bp_has_profile( 'profile_group_id=' . bp_get_current_profile_group_id() ) 

to anything like this

$args = array(
'profile_group_id'=> 'some group_id',
//all other available options are same from the step 2.
);
bp_has_profile( $args ) 

Hope you choose the right approach that suits your need. Please do let me now if you need any further help.

Have a great day.
Anu