Can you inoculate or improve store bought compost?

I'm staring a backyard garden and don't have a lot of inputs to make compost, although I'm going to try regardless. In the meantime I will end up getting store-bought compost, probably by the yard from the municipal program here, to help out my hard clay soil.  My question is: considering that store-bought compost is likely devoid of sufficient bacterial/fungal activity, but still has the proper C:N, pH, friability, etc, can you inoculate it to add the microbial life back?  If so, what can you use?

Attached is the analysis of the compost I'm considering.

Michael,

Welcome to Permies.  Glad to see you starting a garden.  (Please be aware the file you posted has your personal information at top of the report.)

The short answer is yes, of course.  The more complicated answer is how quickly and what are you wanting to improve?  Having a lab soil sample your compost is great idea, but largely unnecessary in my humble opinion.  Give the soil what it needs to promote microbial and bacteria life; and they will take care of your plants.

Year ago, I worked my way through college with my own "landscape" company, meaning I did whatever work in the hot Texas sun that other people would pay me to do; because they did not want to do it.  I had a customer that was an amateur horticulturalist.  He was the best gardener I have seen.  His 'secret'?  I manicured his lawn weekly but was forbidden to remove the clippings.  Everything was dumped on his raised beds, hot composting in the process.  Last weeks clippings were mulch underneath and held the moisture in the Texas heat.  The the clippings from weeks prior had had time to break down and become food for the living biome under in the upper layer of soil.  This weeks clippings made fast heat and kept the weeds from germinating.  

Grass clippings have just about a perfect nitrogen to carbon ratio on their own.  They break down quickly when piled up.  they will simply ignite your colonies of 'good stuff' in the soil.  And the great thing is:  everyweek you can pick up as many bags of the stuff as you want from your neighborhood.  Few resources required.  Try adding grass clippings to your compost or directly to your garden.  You will be amazed at the results.  It may take a season or two to convert the soil (SA is not known for great soil.); but as for amendments to your soil, I would recommend composted grass clippings as a number 1 place to start.

Thanks for the reply.   The analysis was directly from the compost vendor and not my doing.  I will keep a closer eye out for grass clippings.