• Incidence of adverse events [ Time Frame: Minimum of 1 year up to 2 years depending on transplant date ]
  Safety: Since this study is a pilot non-randomized safety and efficacy trial with patient enrollment limited by budgetary constraints, no direct statistical significance tests can be performed.
• Incidence of post-transplant infections and malignancies [ Time Frame: Minimum of 1 year up to 2 years depending on transplant date ]
  Safety: Since this study is a pilot non-randomized safety and efficacy trial with patient enrollment limited by budgetary constraints, no direct statistical significance tests can be performed.
• Incidence of de novo sensitization [ Time Frame: Minimum of 1 year up to 2 years depending on transplant date ]
  Safety: Since this study is a pilot non-randomized safety and efficacy trial with patient enrollment limited by budgetary constraints, no direct statistical significance tests can be performed.
• Incidence of Insulin independence [ Time Frame: Minimum of 1 year up to 2 years depending on transplant date ]
  Efficacy: Incidence of participants no longer using insulin

• Glycemic control [ Time Frame: Day 75, Day 180, Day 270, Year 1, Year 1.5, Year 2 ]
  Assessed by measuring HbA1c using high-performance liquid chromatography
• Glycemic lability [ Time Frame: Day 75, Day 180, Day 270, Year 1 ]
  Assessed with the Mean Amplitude of Glycemic Excursions (MAGE) test
• Hypoglylcemic episodes: Clarke Survey Score [ Time Frame: Day 75, Day 180, Day 270, Year 1 ]
  The Clarke survey will be used to assess the frequency and severity of hypoglycemic episodes
• Hypoglylcemic episodes: Hypo Score [ Time Frame: Day 75, Day 180, Day 270, Year 1 ]
  The HYPO score will be used to assess the frequency and severity of hypoglycemic episodes
• Beta cell function as assessed by Mixed Meal Tolerance Test (MMTT) [ Time Frame: Day 75, Day 180, Day 270, Year 1, Year 1.5, Year 2 ]
  Results from both MMTT and FSIGT will be used to assess beta cell function
• Beta cell function as assessed by Insulin-Modified Frequently-Sampled Intravenous Glucose ToleranceTest (FSIGT) [ Time Frame: Day 75, Day 180, Day 270, Year 1, Year 1.5, Year 2 ]
  Results from both MMTT and FSIGT will be used to assess beta cell function

Single-center, open label, non-randomized safety and efficacy trial to evaluate co-transplantation of allogeneic parathyroid glands (PTG) with adult pancreatic islets (both PTG and pancreatic islets obtained from same deceased donor) in people with Type 1 diabetes in the intramuscular (IM) site with stable function of liver or kidney allografts on chronic immunosuppression.

A total of 8 patients will be enrolled in the study and followed for a minimum of 1 year up to 2 years after the last islet transplant, depending on enrollment date.

Inclusion Criteria:

1. Male and female subjects age 18 or older.
2. Subjects who are able to provide written informed consent and to comply with study procedures.
3. Clinical history compatible with Type 1 diabetes (onset < 40 yrs old and insulin dependent for > 5 yrs at enrollment, c-peptide negative).
4. Recipients should have absent stimulated c-peptide (< 0.3 ng/mL) in response to a (Boost® 6 mL/kg BW to a maximum of 360 mL; another equivalent product), measured at 60 and 90 min after start of consumption.
5. Subjects who are > 6 months post-renal transplant or >6 months post-liver transplant who are taking appropriate calcineurin inhibitor (CNI) based maintenance immunosuppression ([tacrolimus alone or in conjunction with sirolimus, mycophenolate mofetil, myfortic, or azathioprine; or cyclosporine in conjunction with sirolimus, mycophenolate mofetil, or myfortic ± Prednisone ≤ 10 mg/day).
6. Stable renal function as defined by a creatinine of no more than one third greater than the average creatinine determination performed in the 6 previous months prior to islet transplant, as well as absence of a rejection episode in the 6 months prior to islet transplant
7. Stable liver function tests as defined by: SGOT (AST), SGPT (ALT), alkaline phosphatase values < 1.5, or total bilirubin < 1.5 times normal upper limits at time of study entry, as well as absence of a rejection episode in the 6 months prior to islet transplant

Exclusion Criteria:

1. Presence of donor specific anti-HLA antibodies detected by Luminex Single Antigen/specificity bead assay including weakly reactive antibodies that would not be detected by a flow cross match
2. Insulin requirement of >1.0 IU/kg/day
3. Weight more than 100 kg or body mass index (BMI) > 30 kg/m2.
4. Primary hyperparathyroidism OR secondary hyperparathyroidism
5. Untreated or unstable proliferative diabetic retinopathy.
6. Blood Pressure: SBP > 180 mmHg or DBP >100 mmHg despite treatment with antihypertensive agents.
7. Calculated GFR of ≤ 40 mL/min/1.73 m2 using the subject's measured serum creatinine and the Chronic Kidney Disease Epidemiology Collaboration (CKD- EPI) equation, as well as presence of a rejection episode in the 6 months prior to islet transplant
8. Elevated liver function tests as defined by: SGOT (AST), SGPT (ALT), alkaline phosphatase values > 1.5, or total bilirubin >1.5 times normal upper limits at time of study entry, as well as presence of a rejection episode in the 6 months prior to islet transplant
9. Proteinuria (albumin/creatinine ratio or ACr > 300mg/g) of new onset since kidney transplantation.
10. For female subjects: Positive pregnancy test, presently breast-feeding, or unwillingness to use effective contraceptive measures for the duration of the study and 4 months after discontinuation. For male subjects: intent to procreate during the duration of the study or within 4 months after discontinuation or unwillingness to use effective measures of contraception. Oral contraceptives, Norplant®, Depo- Provera®, and barrier devices with spermicide are acceptable contraceptive methods; condoms used alone are not acceptable.
11. Active infection including hepatitis B, hepatitis C, HIV, or TB. Quantiferon gold assay will be used to determine TB infection.
12. Invasive aspergillus, histoplasmosis, and coccidioidomycosis infection within 1 year prior to study entry.
13. Any history of malignancy following receiving either the kidney or liver transplant, except for completely resected squamous or basal cell carcinoma of the skin
14. Known active alcohol or substance abuse.

15. Severe co-existing cardiac disease, characterized by any one of these conditions:

    1. Recent MI (within past 6 months),
    2. Evidence of ischemia on functional cardiac exam within the last year,
    3. Left ventricular ejection fraction < 30%,
    4. Valvular disease requiring replacement with prosthetic valve.
16. Active infections (except mild skin and nail fungal infections).
17. Active peptic ulcer disease or gastritis, symptomatic gallstones, or portal hypertension.
18. Use of any investigational agents within 4 weeks of enrollment.
19. Administration of live attenuated vaccine(s) within 2 months of enrollment.
20. Any medical condition that, in the opinion of the investigator, will interfere with safe study completion.
21. Positive screen for BK viremia at time of screening.
22. Untreated hyperlipidemia - TC > 200 mg/dL, TGC > 200 mg/dL, LDL > 130 mg/dL