Sorry Manch, when I was calling it the "LLE" that we could offer House, I was referring to that Bi-Annual exception. Should have made that clear.
That said, even without using the Bi-Annual or Mid Level exception, I guess we can sign House for up to $1.8 million next year. From the same Wikipedia page:
Non-Bird exception
Free Agents who qualify for this exception are called "non-qualifying free agents" in the CBA, meaning they do not qualify under either the Larry Bird Exception or the Early Bird Exception. Under this exception, teams can re-sign a player to a contract beginning at either 120% of his salary for the previous season, or 120% of the league's minimum salary, whichever amount is higher. Contracts signed under the Non-Bird exception can last up to six years.
Similarly, we could resign Posey for up to $3,847,200 next year using the same exception. However, we couldn't really give him a long term deal, since after the first year's 20% raise from this year, we could only include 8% raises in the following years, meaning the best we could offer is something like 5 years, $22.5 mil or 4 years, $17.25 mil, something I think other teams could beat.