Inclusion Criteria:
* Age \>= 5 years and \< 10 years
* Tanner stage 1
* Clinical Diagnosis of MPS IVA or VI
Subjects will be stratified into 2 groups:
* MPS IVA (3 patients)
* MPS VI (3 patients)
* MPS Diagnosis Confirmed by either:
1. Demonstration of 2 pathogenic or likely pathogen mutations (or homozygous for single mutation) and elevated GAG (either before or during ERT treatment), OR
2. Demonstration of diagnostic enzyme deficiency, elevated GAG (either before or during ERT treatment), and a normal second sulfatase
* Currently receiving ERT \[elosulfase alfa (Vimizim®) or galsulfase (NAGLAZYME®)\] for minimum of 12 months prior to study entry
* HSCT greater than 3 years before entry
* Height Z-score \<-2.0 or less than 2 cm change in height velocity over the last 1 year
* Willing to consent to the study and comply with all study procedures and assessments
* Able to stand independently without hand support for minimum of one minute
* Guardians able to successfully administer investigational drug daily/SQ
Exclusion Criteria:
* ERT naïve
* Poor compliance with ERT (\<75% in 6 month period)
* Diagnosis with growth hormone deficiency (defined by IGF-1 SDS \<-1.0 according to age, gender and tanner stage)
* Hypothyroidism, untreated (TSH \>4.0 mU/L)
* Receiving or has received growth hormone therapy, IGF-1 therapy, anti-TNF alpha therapy, angiotensin-converting enzyme (ACE) inhibitors, angiotensin II receptor blockers, diuretics, beta-blockers, calcium channel blockers, cardiac glycosides, systemic anticholinergic agents, any medication that may impair or enhance compensatory tachycardia, diuretics or other drugs known to alter renal or tubular function within the previous 6 months.
* Receiving or has previously received a GnRH analog (e.g. leuprolide acetate, histrelin)
* History of malignancy
* History of chronic inflammatory condition not related to MPS
* History of conditions/medical therapies that might affect the interpretation of growth results such as anemia, celiac disease, diabetes, inflammatory bowel disease, and cystic fibrosis
* QTC (Fridericia) \> 450 msec
* Malnutrition (BMI \<5th percentile)
* History of gene therapy
* Concurrent participation on an investigational drug trial
* Investigational drug washout minimum of 5 half-lives of the drug or 1 month whichever is longer
* Previous or current treatment with the investigational drug (vosoritide)
* Known or suspected allergy to the investigational drug (vosoritide)
* Bone fracture within the previous 6 months
* Skeletal surgery within the previous 6 months, or anticipated significant surgery (in the view of the investigator) during course of the study
* Any history of bone lengthening surgeries or spine fixation surgery
* Spine curvature (scoliosis) on previous x-ray greater than 25 degrees
* Untreated severe sleep apnea
* History of chronic renal insufficiency, defined previously as an eGFR \<60 mL/min/1.73m2
* Illness that could affect blood pressure / orthostatic problems
* Treated with medications known to affect QC/QTc
* LV Ejection fraction \<40%; LVEF=\[SV/EDV\] x100 (American Society Echocardiography)
* Treated with chronic oral steroids in previous 6 months
* Mean SpO2 of \< 92% at baseline, taken from average of 3 measurements in each hand
* Concurrent disease or condition that in the view of the investigator, would interfere with study participation or safety evaluations, for any reason.