Combination of Biologic and Anti-obesity Therapies in Psoriatic Arthritis

Inclusion Criteria: 1. Age \>= 18 years and \<=75 years 2. Have a documented diagnosis of PsA for at least 6 months AND fulfil the CASPAR criteria (Defined as \>=3 points) 3. Have active PsA defined as \>=3 swollen and \>=3 tender joints (dactylitis counts as a swollen joint). 4. Have a BMI \>= 27 kg/m\^2 5. Have at least one affected joint amenable to ultrasound-guided synovial biopsy (and must undergo successful synovial biopsy prior to randomisation) 6. Have at least one psoriatic plaque amenable to biopsy (up to a maximum of 5 participants per treatment arm can be recruited without skin biopsy if no suitable lesion 7. Capable of giving signed informed consent 8. Willing and able to participate in the study and undergo synovial, adipose and skin (if appropriate) biopsies (under local anaesthetic) on at least 2 occasions Exclusion Criteria: Prior/Concomitant Therapy: 1. Previous treatment with tirzepatide or any GLP-1 receptor agonist. 2. Previous treatment with Ixekizumab. 3. Previous treatment with BOTH secukinumab AND Bimekizumab. \[note: Previous treatment with one of EITHER secukinumab OR Bimekizumab for PsA/psoriasis is allowed PROVIDED: i) Last dose was \>6months before baseline AND ii) Therapy was not stopped due to an IL-17-related side effect OR due to complete primary lack of response. 4. Previous treatment with rituximab. 5. Failed \>3 classes of advanced therapies (regardless of given for PsA or psoriasis), including but not limited to: * TNF inhibitors (adalimumab, etanercept, certolizumab, golimumab, and infliximab) * IL-12/23 inhibitors (ustekinumab) * IL-23 inhibitors (guselkumab and risankizumab) * IL-17 Inhibitors (secukinumab or bimekizumab) * Selective co-stimulation modulators (abatacept) * Janus Kinase or tyrosine kinase 2 inhibitors (tofacitinib, upadacitinib and deucravacitinib) Note: Prior exposure to phosphodiesterase-4 inhibitors, such as apremilast and conventional synthetic DMARDs, such as methotrexate, are not considered as advanced therapies. 6. If currently receiving conventional DMARDs, or apremilast, must have been treated for at least 12 weeks prior to first biopsy visit and on a stable dose for at least 8 weeks prior to first biopsy visit. 7. Use or oral, intra-articular, IM or IV corticosteroids 4 weeks prior to first biopsy visit or anticipated/planned prior to the week 12 biopsy visit. 8. Topical steroids within 2 weeks of first biopsy visit (participants on topical corticosteroids at baseline willing to leave these off 2 weeks prior to biopsy will be eligible). 9. Live, attenuated or recombinant vaccination within 1 month prior to screening visit or planned before the 12 week visit. 10. Contraindication to local anaesthetics (lidocaine/similar) used for biopsies 11. Antiplatelet or anticoagulant therapy that cannot be safely interrupted: 1. Clopidogrel or other antiplatelet therapies (note: aspirin is not an exclusion) 2. Vitamin K antagonists (including but not limited to warfarin) 3. Direct inhibitors of thrombin (e.g. dabigatran) 4. Factor Xa inhibitors (e.g. rivaroxaban, apixaban) 5. Heparins (including low-molecular weight heparins (LMWH) 12. Previous treatment with insulin (exception: Use of insulin for gestational diabetes or short-term use (less than 14 days) for acute conditions, such as acute illness, hospitalisation or elective surgery). Medical Conditions: 13. Diagnosis of type 1 diabetes or insulin treated type 2 diabetes. 14. History of severe hypoglycaemia and/or hypoglycaemia unawareness within the 6 months prior to screening. 15. History of ketoacidosis or hyperosmolar state or coma in the last year 16. Any current or past diagnosis of: * proliferative diabetic retinopathy, or * diabetic maculopathy, or * non-proliferative diabetic retinopathy that requires treatment. 17. Have a self-reported change in body weight greater than 5% (gain or loss) within 3 months prior to screening. 18. Prior or planned surgical treatment for obesity, such as gastric bypass (bariatric) surgery or restrictive bariatric surgery (excluding liposuction or abdominoplasty if performed more than 1 year prior to screening). 19. Have a family or personal history of medullary thyroid carcinoma or multiple endocrine neoplasia (MEN) syndrome type 2. 20. History of IBD (Crohn's disease or ulcerative colitis). 21. Known clinically significant gastric emptying abnormality (for example, severe gastroparesis or gastric outlet obstruction); or chronically take drugs that directly effect gastroparesis. 22. History of chronic or acute pancreatitis. 23. Renal Impairment with estimated glomerular filtration rate (GFR) of less than or equal to 30ml/min/1.73m\^2. 24. A diagnosis or history of malignant disease within 5 years prior to baseline visit, with the following exceptions: * Basal cell and squamous epithelial carcinomas of the skin that have been resected, with no evidence of metastatic disease for 3 years and 2 years, respectively. * cervical carcinoma in situ, with no evidence of recurrence within 3 years. 25. History of any other condition (such as known drug, alcohol abuse, or psychiatric disorder) that, in the opinion of the investigator, may preclude the participant from following and completing the study. 26. History of significant active or unstable major depressive disorder (MDD), suicidal ideation, or other severe psychiatric disorder (for example, schizophrenia, bipolar disorder, or other serious mood or anxiety disorder) within the last 2 years. Note: Participants with MDD or generalised anxiety disorder whose disease state is considered stable for the past year and expected to remain stable throughout the course of the study, in the opinion of the investigator, may be considered for inclusion if they are not on excluded medications. 27. Are, in the judgement of the investigator, actively suicidal or deemed to be at significant risk for suicide. 28. Diagnosis of other inflammatory arthritis, such as rheumatoid arthritis, ankylosing spondylitis, reactive arthritis, gout, or enteropathic arthritis. 29. Active infection at screening. 30. Have had any of the following types of infection within 3 months prior to screening or develops any of the following infections before the baseline visit: * Serious (requiring hospitalisation, or intravenous or equivalent oral antibiotic treatment, or both). * Opportunistic. Note: Herpes Zoster is considered active and ongoing until all vesicles are dry and crusted over). * Chronic (duration of symptoms, signs and/or treatment of 6 weeks or longer). * recurring (including, but not limited to, herpes simplex, herpes zoster, recurring cellulitis, and chronic osteomyelitis). 31. Have evidence or suspicion of active or latent TB (unless screened previously, all will be evaluated for TB prior to initiating treatment) or had latent TB infection that has not been treated with a complete course of appropriate therapy as per local guidelines, unless such therapy is currently underway. 32. Current HIV infection. 33. Current infection with hepatitis B virus (HBV) (i.e. positive for HBsAg and/or PCR positive for HBV DNA). 34. Current infection with hepatitis C virus (HCV) (i.e. positive for HCV RNA). 35. History of recurrent or chronic infection which in the opinion of the investigator might place a participant at unacceptable risk for participation in the study. 36. Major surgery witing 8 weeks prior to screening or planned within 12 weeks from baseline visit. 37. Any other condition that is a contraindication to ixekizumab or tirzepatide. Laboratory results: 38. If type 2 diabetic, laboratory evidence of poorly controlled diabetes, including HbA1c \>80mmol/mol (\>9.5%). 39. Clinical laboratory test results at screening that are outside the normal reference range for the population and are considered clinically significant, or have any of the following specific abnormalities: * Absolute neutrophil count \<1.5 x 10\^3/microlitre * Lymphocyte count \<0.80 x 10\^3/microlitre * Platelet count \<100 x 10\^3/microlitre * Total WBC count \<3.00 x 10\^3/microlitre * Haemoglobin \<85 g/L (males) or \<80g/L (females) * AST or ALT levels \>3 x upper limit of local normal range * Serum creatinine levels \>2.0omg/dL (equivalent to \>176.8 micromol/L Participants who fail screening as a result of a minor blood test abnormality/abnormalities may be re-screened and have the test(s) repeated, within 14 days of the previous blood test, at the investigators discretion. If the tests meet the trial entry criteria on the second occasion, then the participant will be deemed to meet the entry criteria for the trial. In women of child bearing potential(WOCBP): 40. Are Pregnant, breastfeeding or planning to become pregnant during the course of the study. 41. Not established, or unwilling to use a method of contraception considered highly effective for the duration of the study and at least 4 weeks after the study if they receive tirzepatide, or 10 weeks if they receive ixekizumab. Tirzepatide may decrease the effectiveness of oral contraceptives, so it is advised that WOCBP using an oral contraceptive should add a barrier method of contraception or switch to a non-oral contraceptive method for the first 4 weeks of treatment, and for 4 weeks after each dose increase. Other exclusions: 42. Have participated, within the last 30 days prior to trial entry, in a clinical study involving an investigational study intervention. If the previous investigational study intervention has a long half life, then 5 half lives or 30 days (whichever is longer), should have passed prior to screening. 43. Are currently enrolled in any other clinical study involving an investigational study intervention or any other type of medical research judged not to be scientifically or medically compatible with this study. 44. Unable or unwilling to provide informed consent. 45. Are unsuitable for inclusion in the study, in the opinion of the investigator or sponsor, for any reason that may compromise the participant's safety or confound data interpretation. 46. Any other contra-indications to biopsies (including anti-coagulants) in the opinion of the investigator.