Better way than multiple JOINs to same table?

I am looking for a better way to write this query. 

The query uses the results from a CTE created previously which has these columns:

		(	 
			 TravelerID
			,FirstName
			,LastName
			,Company
			,PlacementID
			,PlacementSkillSet
			,StartDate
			,EndDate
			,WksOnAssignment
			,Recruiter
			,DisciplineID
			,SpecialtyID
			,BookingCompanyID
		)

TravelerID	FirstName	LastName	Company	PlacementID	StartDate	EndDate	CompanyID	FacilityID
65648	Lori	SmithAcme	392605	2/24/03	5/24/03	3	3397
65648	Lori	Smith	Acme	477950	5/26/03	11/22/033	282
65648	Lori	Smith	Acme	600089	12/1/03	5/29/04	3	282
65648	Lori	Smith	Acme	717424	5/30/04	12/4/04	3	282
65648	Lori	Smith	Acme	832842	12/5/04	2/4/05	3	282

This is a list of all the placements the person has been on. What they want to do is count placements where there is only a gap of one day between the previous placement's EndDate and the new placement's StartDate at the same Facility as one placement. Notice in the list above, PlacementIDs 600089, 717424, and 832842 are all consecutive, so they want them to be one placement. I need to still get the first StartDate and the last EndDate of that series, so it would look like so:

TravelerID	FirstName	LastName	Company	PlacementID	StartDate	EndDate	CompanyID	FacilityID
65648		Lori		Smith		Acme	392605		2/24/03		5/24/03	3		3397
65648		Lori		Smith		Acme	477950		5/26/03		11/22/033		282
65648		Lori		Smith		Acme	600089		12/1/03		2/04/05	3		282

It could be 2 consecutive placements, or it could be 20 that make up one placement, the amount would vary. My query is joining the same CTE four times to itself, but that would not be reliable (what if there were 5 consecutive placements?). 

SELECT   
		 v1.TravelerID
		,v1.FirstName
		,v1.LastName
		,v1.Company
		,v1.PlacementID
		,v1.PlacementSkillSet
		,v1.StartDate
		,COALESCE(v5.EndDate, v4.EndDate, v3.EndDate, v2.EndDate, v1.EndDate) AS EndDate
		,ISNULL(v1.WksOnAssignment,0) + ISNULL(v2.WksOnAssignment,0) + ISNULL(v3.WksOnAssignment,0) + 
		 ISNULL(v4.WksOnAssignment,0) AS WksOnAssignment
		,v1.Recruiter
		,v1.DisciplineID
		,v1.SpecialtyID
		,v1.BookingCompanyID
		,v1.PlacementID
		,v2.PlacementID
		,v3.PlacementID
		,v4.PlacementID
FROM CTE_All v1
JOIN CTE_All v2 ON v1.TravelerID = v2.TravelerID
						AND v1.FacilityID = v2.FacilityID
						AND v1.StartDate < v2.StartDate
						AND v1.EndDate < v2.EndDate
						AND v2.StartDate = v1.EndDate + 1
LEFT JOIN CTE_All v3 ON v3.TravelerID = v2.TravelerID
						AND v3.FacilityID = v2.FacilityID
						AND v3.StartDate > v2.StartDate
						AND v3.EndDate > v2.EndDate
						AND v3.StartDate = v2.EndDate + 1
LEFT JOIN CTE_All v4 ON v3.TravelerID = v4.TravelerID
						AND v3.FacilityID = v4.FacilityID
						AND v3.StartDate < v4.StartDate
						AND v3.EndDate < v4.EndDate
						AND v4.StartDate = v3.EndDate + 1
)

I was thinking there should be a smarter way to do this. Please help

Thanks all!!!