Creating new date variables and a flag for rolled up dates SAS 9.4

[Whitlea]

In my code below I am rolling up dates of service that are less than 7 days apart into 1 stay for each ID and creating a new date span with my span_begin and span_end variables based off of the first and last date of service. My flag is a stay indicator variable that identifies the final stay dates I want to use in my final analysis.  My code below almost does what I want but I noticed that some clients who have back to back stays in different clinics are not getting flagged or the date spans the way I want them to. For example (see code below), I need ID "C" to have 2 stays/flags, one for clinic 3 and one for clinic 4 so I need to include the clinic in the code but was unable to do this without making a mess of things. 

Note: 

Each ID can have more than one stay in the same clinic and/or in a different clinic. 

All dates of service <7 days apart are rolled up into one stay for each ID unless they are moved into a different clinic. If they move into a new clinic that would count as a new stay with a new span_begin and span_end.

FDOS=first date of service

LDOS=last data of service

These are the results I am getting:

This is what I want:

Data Have;

input ID$ Clinic$ FDOS :DATE9. LDOS :DATE9.;
format FDOS MMDDYY10. LDOS MMDDYY10. ;
datalines;
A	1	22Jul2022	19Sep2022
A	1	20Sep2022	19Oct2022
A	1	20Oct2022	24Oct2022
B	2	1Jul2022	1Jul2022
B	2	2Jul2022	15Jul2022
B	2	16Jul2022	22Jul2022
B	2	23Jul2022	23Jul2022
B	2	24Jul2022	31Jul2022
B	2	1Aug2022	15Aug2022
B	2	16Aug2022	30Aug2022
B	2	31Aug2022	31Aug2022
B	2	1Sep2022	2Sep2022
B	2	3Sep2022	4Sep2022
B	2	5Sep2022	15Sep2022
B	2	16Sep2022	29Sep2022
C	3	6Mar2023	31Mar2023
C	3	1Apr2023	4Apr2023
C	3	5Apr2023	30Apr2023
C	3	1May2023	4May2023
C	3	5May2023	31May2023
C	3	1Jun2023	3Jun2023
C	3	4Jun2023	7Jun2023
C	4	8Jun2023	30Jun2023
D	5	1Jul2022	15Jul2022
E	5	5Apr2023	15Apr2023
E	5	16Apr2023	30Apr2023
E	5	1May2023	4May2023

;
run;

Proc sort data=Have;
by  ID FDOS LDOS;
run;

data Span;
set Have;
by  ID FDOS LDOS;
retain Span_Begin;
l_last = lag(LDOS);
if first.ID then Span_Begin=FDOS;
else if FDOS - l_last > 7 then do;
Span_Begin=FDOS;
end;
Span_End=LDOS;
format Span_Begin mmddyy10. Span_End mmddyy10. ;
run;

proc sort data=Span;
by ID Span_Begin Span_End;
run;

data Flag;
set Span;
by ID Span_Begin Span_End;
flag=last.Span_Begin;
run;

proc print data=Flag;
var  ID Clinic Span_Begin Span_End flag ;
run;

[ballardw · Accepted solution]

Sort the data by Id Clinic then the dates.

Add Clinic to the BY statement in the data step.

Do the spans based on first.Clinic instead of first.Id