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People in the above thread were unsuccessful upgrading to 2nd and 3rd gen parts.
Link from above thread listing potentially supported CPUs
en.wikipedia.org
However, the only ones guaranteed to work are the ones that toshiba says works. I don't know if Toshiba lists any supported CPUs or even has the product information for your laptop, but I would check there first. I'm having a hard time finding information on the l775-197, but you can check your product/serial number at their website to see if you have any luck.
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Looks like you're probably stuck with a 1st gen i7. If it's a first gen i3 (35W), then it probably comes with the i3 380m? Unless your laptop has a lot of thermal headroom, you might want to stick with a 2C/4T part, since all of those are 35W. There are some 4 core parts, though their TDP ranges from 45-55w.
Moving to a dual core i5/i7 part mostly gets you turbo. moving to a 4 core part is risky and depends on the cooling solution in the laptop. FYI from a quick google search, it doesn't look like the l775 line was ever sold with a 45W+ processor.