Rather than save money, would it be wise to invest money into a constantly expanding portfolio?

And I am talking about individual stocks, not mutual funds. I am talking about let's say that every couple months you buy $1000 worth of a small company that has a high rating and shows some potential. And then you just let it sit for the long term come hell or high water (unless they go bankrupt or lose 35% or... show more And I am talking about individual stocks, not mutual funds. I am talking about let's say that every couple months you buy $1000 worth of a small company that has a high rating and shows some potential. And then you just let it sit for the long term come hell or high water (unless they go bankrupt or lose 35% or more of what you invested). And you just keep doing this, expanding your portfolio every couple months by buying another type of stock in another company.

Is that wise or do you see some flaws that need worked out in that reasoning?
Update: Let's say you expand it to about 10 or 15 stocks, and then just start to beef them up even more?
Update 2: Or perhaps 20 or so.
5 answers 5