Are there doctors in the USA that do high volume liposuction (more than 4 liters)?

You need to be evaluated in person. First thing to know is that liposuction is not for weight loss and it only removes localized fat under the skin. Like deflating a balloon. The more the balloon is deflated, the more wrinkly its surface gets: that would be your extra skin that has been stretched. A board certified plastic surgeon can assess if liposuction is a good option for you and then decide on the volume to be safely removed. 

Thank you for your question. To provide a valid medical opinion I will need to see pictures of you body from different angles. I would suggest to be treated by board certified plastic surgeon with experience in this procedure, to get the best desired results.
Respectfully,Dr. Emmanuel Mallol Cotes.-

Most surgeons will hold the liposuction to 5 liters in the outpatient setting except in Florida where the limit is 4L. You are on the right course of losing weight to bring your BMI of 37.4 closer to 30 to maximize results and reduce the risks of complications during and after surgery. Liposuction is not to be considered a weight loss procedure but a contouring one.

In the US its recommended to stay under 5L, which we do frequently. Although liposuction is not a weight loss procedure you can do numerous treatments plus hormonal optimization for weight loss and get a good results.  You need a consult.
You need a formal evaluation by an expert in body shaping and contouring to determine what is best.  Traditional liposuction awake and smart liposuction are old methods and do very poorly for tightening skin or significant skin tightening or contouring.  Small problem areas can be improved slightly by these methods.  The best in body contouring not only removes fat with energy devices like VASER ultrasound but also internally heat the skin with radio-frequency devices such as J PLASMA/RENUVION, InMode BodyTite, ThermiRF to heat the under surface of the skin and tighten it at the same time as fat removal. These combinations are called 4D HIDEF VASER contouring and can only be done by a well . trained body contouring specialist. At the same time fat should be harvested, PRP and stem cells added and injected into muscles or indentations/cellulite to get body shaping and contouring.  This is known as a Brazilian butt lift when you inject the fat to the buttock for contouring and lifting, but fat can also be used in areas such as the chest/breast, arms/shoulders, calves and face.  Cellulite should also be treated with cellfina, sculptra, subcision and/or fillers such as bellafill, renuva synthetic fat, or sculptra.  If skin is very loose before surgery then it will need to be removed such as lower abdominal skin (tummy tuck/abdominoplasty), breast skin (breast lift), arm skin (brachioplasty).  Overall you need a full assessment, but simple liposuction alone will not tighten skin and needs a combination of various methods -- fat removal, skin tightening, defining, fat grafting, skin removal -- to get the best in body contouring and body sculpting.  Dr. Emer.

At BMI over 37- a person is considered obese. You should not consider liposuction at this time, instead focus on loosing significant weight, focus on healthier lifestyle, and once you achieve a healthy weight -then re-assess your goals. Liposuction/ liposculpture  is a body contouring operation, not a weight loss operation.