The short story is that it is not very likely.
Our ability to sign an additional free agent to a maximum contract depends entirely on whether the salary cap goes up or down, and by how much.
As I have described before, it is almost certain to decrease.
Let's keep the math simple:
If we want to sign two free agents with seven years of experience to maximum contracts, then we will dedicate 30% of our salary cap to each of these guys in the first year - meaning that 60% of our salary cap will be tied up with two guys.
That leaves 40% for everyone else.
Now: during the summer of 2010, we will likely have Daniel Gibson, Maurice Williams, Darnell Jackson, Delonte West, and J.J. Hickson under contract. (It is possible that we could waive J.J. Hickson after two years, and Delonte has a team option in 2010 - it is possible that we could forgo the team option. It is not clear to me, but Darnell could have a player option too. But getting rid of all of these guys is very unlikely.)
If you add up the contracts of these five players, they will make a collective $20.2M - $20.4M, depending on which set of published contract data you believe. In addition, we have to add the minimum salaries of five "phantom" players, as the salary cap must accommodate 12 players at a time. Add an additional $2.37M for those five "phantom" players, and it means that we will have a minimum cap number of $22.6M - $22.8M for 2010.
Divide those numbers by 0.4, because those salaries can only accommodate 40% of our total salaries, and you will realize that the salary cap must be between $56.5M - $57M for 2010 for us to be able to sign two players.
In my previous post, I have explained why that is unlikely. If the salary cap decreases by only 2% per year for the next two years, we will not be able to accommodate two maximum player salaries.
However, we should also understand that we are going to have two first-round draft picks in the next two years. It is possible that we could stash them both in Europe, and they would therefore not count against our salary cap in 2010, but that is probably unlikely. And we will also need to re-sign Andy Varejao. Assuming we sign Andy and our draft picks, our cap number will probably be on the order of about $31M - $32M - which certainly will not leave enough to sign another maximum contract free agent besides LeBron.
Now. We could gut our team and keep only Mo Williams, Boobie Gibson, and eight "phantom contracts" for 2010. If we did that, we could conceivably get our cap number down to $17.1M, and the salary cap would have to be more than only $43M to sign two maximum players. So there is a theoretical possibility that we could do it, but ask yourself - do you really want to go to battle with LeBron, Bosh (or another max player), Mo, Boobie, and eight minimum level players?
Add it up and it is extremely unlikely that we will be able to pull off another maximum contract in 2010.