You always get a better job with a tear off. You may be at the maximum number of layers, I don't know, but if so a lay over may be illegal.
There's no reason to isntall ice shield and then modified unless the salesman is uneducated and thinks the self adhering base sheet is ice shield. I'm not a fan of modified anymore but when installed properly can be a fine roof. I'm also not a fan of isntalling torch on modified without some kind of cover board over the wood substrate, assuming it is a wood substrate. Be very careful when playing with fire.
There's nothing wrong with EPDM, but I prefer TPO because of the heat welded seams. TPO has an iffy reputation with some early failures. PVC has a good reputation, like epdm, and heat welded seams like TPO, so it's a win win. But PVC costs more than TPO or EPDM.
Here is another thing to consider. Where do you live? Reflectivity may be an important concern for energy effeciency reasons. TPO is usually white, though available in other colors. And EPDM is usually black, though available in white for an upcharge. White is reflective and is pretty much the norm for a majority of the flat roofs we install.
The roof is more than just the membrane. God I am getting tired of typing this out every day, there are a dozen posts with similiar information, but here gos anyways. The roof is more than just the membrane. It is also possibly cover board, possibly insulation, possibly ventilation, and all the details. The details include wall terminations, pipe flashings, drainage and/or gutter and more and more. It's the accessories and details that really make up the roof. Neglect one detail and a flat roof will leak. Neglect an essential accessory and the roof won't last as long as intended. In comparing proposals from licensed and certified roofing contractors, you must consider ALL variables, not just the membrane.
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If you have existing epdm, it should last longer than 11 years WHEN PROPERLY INSTALLED. Even 45 mil should last longer than 11 years. You may benefit from a seam and penetration restoration, the epdm membrane may be in good shape. The EPDM should last forever, it's the seams and adhesives that fail. If the roof was poorly installed you can't blame the membrane.