You sound very new to investing, here below is a list of things to consider and use as points of study. After that I'll tell you how stocks and markets ARE manipulated and show a way that some entities use to do this.
1- What you are proposing is a felony (conspiracy to manipulate the market) and if caught, you and anyone else involved would be subject to fines and/or prison. The street term for what you describe is a "wash trade" or "churning". I believe the price would rise but not the way you think it could.
2- A company with $20M in market capitalization is considered a Micro-cap- No where near a Mid- cap- These usually trade on the OTC exchange at one of several levels that have been established to reflect the current financial and regulatory status of a particular company.
2a- Most OTC stocks are thinly traded, which means the spread between the buy price and the sell price can be much larger than is seen on the major exchanges. There are a few which are more active and so may have a smaller spread.
3- Your broker is not typically the entity matching orders. In-house routing is done at some brokerages but even with that. What I describe below is likely to happen "in house" as well, and legitimately as there is no spread between the prices of your $3.00 attempted transaction so the "duty to improve" wouldn't require the match of 2 orders with the same price and they would likely improve your buddies price as well as the price of another client selling.
3a It is the Market Specialist or Market Maker (MM) for that stock (perhaps only one with the stock you describe). Market Makers among other things are able to buy and sell stock- - They are tasked to keep an orderly market in certain investment vehicles including stock(s). MMs typically make their money through the spread. That is the difference between the buy and sell price- you are probably used to seeing a small spread and depending on the type of access you have to markets, usually level 1 or level 2 at your brokerage. For the OTC info go to their site. MMs have books with current buy and sell orders.
OK here is the "bit" I think what would likely happen is the MM would sell stock to your friend, from his own inventory, or sell short and then replace with shares purchased from the order book. MMs are also able to make money in this manner. The bid priced would be improved to some degree to make the transaction legal. This could have the tendency to raise the price depending on the amount of money involved- It might be replaced with a single order if your buddy was only dealing with a few thousand shares (not much impact). If it was for a larger order and selling lots were being taken out then the price would increase naturally, be cause the deeper into the book the MM had to go the higher the asking prices would be. If the book was used up the MM might go to a friend or other place or might go to the market and prices would pick up where the book left off.
Market Manipulation is something that happens everyday in the markets- usually done by large entities/participants with impunity. An individual attempting to do the same thing probably would have a higher chance of being caught... There is constant complaining about lack of FTC oversight etc. It is way too much to go into here but all of the info (pro and con) is out there if you are really interested.
"Search engines are your friends"-
"When it comes to questions about the market there is one ultimate answer 90% of the time- MONEY!"
Best Regards Indie_Indeep