Can an investment club, made up of non-accredited investors, invest in multiple startups?

You can invest in whatever you want :-).

It's the startups that will get in hot water if they take your money, since you're not accredited investors, http://www.sec.gov/answers/accred.htm

a charitable organization, corporation, or partnership with assets exceeding $5 million;

a director, executive officer, or general partner of the company selling the securities;

a business in which all the equity owners are accredited investors;

a natural person who has individual net worth, or joint net worth with the person’s spouse, that exceeds $1 million at the time of the purchase, excluding the value of the primary residence of such person;

a natural person with income exceeding $200,000 in each of the two most recent years or joint income with a spouse exceeding $300,000 for those years and a reasonable expectation of the same income level in the current year; or

It's an interesting question but the answer to that is quite likely no.

You can look at this page to make a determination whether you will need to register with the SEC.

What you do have to check upon is whether or not there are any state registrations that might be required for your club.

Investment clubs can invest in any instrument and/or company they choose. Just be sure to keep good records.

http://www.bivio.com/bp/Tour_How_Will_bivio_Make_It_Easier_To_Run_A_Club

One thing that I've learned being the president of an investment club is that the SEC is like the IRS. As long as you're small and keep good records, you're relatively safe. The more money you manage and invest, the more likely you are to come under suspicion of the SEC. But as long as you don't show any hint of purposely trying to circumvent the law, the SEC won't really have a problem with you... there are bigger fish in the sea.

Whether you're accredited investors or not, that's a tax situation for the start-ups themselves to work out.

New exemptions have emerged from the JOBS Act: http://en.wikipedia.org/wiki/Jumpstart_Our_Business_Startups_Act

"To provide a new exemption from the requirement to register public offerings with the SEC, for certain types of small offerings, subject to several conditions. This exemption would allow use of the internet "funding portals" registered with the government, the use of which in private placements is currently extremely limited by current law. One of the conditions of this exemption is a yearly aggregate limit on the amount each person may invest in offerings of this type, tiered by the person's net worth or yearly income. The limit ranges from 2% of people earning (or worth) up to $40,000, up to a cap of $10,000 for people earning (or worth) $100,000 or more. This exemption is intended to allow a form of crowd funding).[13] While there are already many types of exemptions, most exempt offerings, especially those conducted using the internet, currently are offered only to accredited investors, or limit the number of non-accredited investors who are allowed to participate, due to the legal restrictions place on private placements of securities."