There are a few funds that publicly accept money for their existing funds. For example, alumni ventures https://www.av.vc/av-funds. They have multiple funds and one (meaning any individual) can choose which fund to invest in. 
1- is that not considered general solicitation because the fund already exists? But if the fund already exists, then its size is already known so when they raise more money for the same fund, then why doesn't it qualify as a new fund, which means they should not do general solicitation? 
2- The minimum check size for alumni ventures is 10K. How ae they able to do that given there is overhead associated with getting small checks from LPs?