Run multiple synchronous and asynchronous test suites in different threads

Question

In my testng, i have multiple test suites. For an e.g.

<suite name="Suite">
   <suite-files>
      <suite-file path="ASynchronousTestfile1.xml"/>
      <suite-file path="SynchronousTestfile2.xml"/>
      <suite-file path="SynchronousTestfile3.xml"/>
   </suite-files>
</suite>

Now, to run suites on separate testng threads. I am using surefire plugin config to run it on separate threads. Something like this :

<configuration>
   <suiteXmlFiles>testng.xml</suiteXmlFiles>
   <skipTests>false</skipTests>
   <properties>
      <property>
         <name>suitethreadpoolsize</name>
         <value>3</value>
      </property>
   </properties>
</configuration>

Now since my ASynchronousTestFile1.xml has non-dependent test cases, i want this test suite to run on multiple threads. So i provided test level parallelism on the suite itself by :

<test name="All Asynchronous Tests" parallel="methods" thread-count="7">

So my perception was there will be total 9 threads, where 2 will be defined to 2 synchronous suites and 7 thread for the Asynchronous test suite.

Where i am missing or what is the correct way of achieving such case ?