There is no written test for the multi, you are already a private pilot, this is considered an add-on rating.
You should be able to get this rating in about 10-15 hours, then start work on your instrument.
The time it will take will be somewhat dependent on if you are enrolled Part 141 or Part 61 and how many hours you have to burn to get to 190 or 250 respectively.
Figure 40 hours for the instrument, knowing that some of that time can be shaved down in the simulator.
Figure about another 40 hours for the commercial, but some of that can be considered time building, you should be able to qualify for the test in quite a bit less than that.
You should be able to get this rating in about 10-15 hours, then start work on your instrument.
The time it will take will be somewhat dependent on if you are enrolled Part 141 or Part 61 and how many hours you have to burn to get to 190 or 250 respectively.
Figure 40 hours for the instrument, knowing that some of that time can be shaved down in the simulator.
Figure about another 40 hours for the commercial, but some of that can be considered time building, you should be able to qualify for the test in quite a bit less than that.