Personally I am applying for some grants to extend my postdoc. My boss will only let me apply for one at a time. Some funding are like papers and don't like your proposal to be under consideration elsewhere.
His view is that it would look quite bad to apply for two grants, get both and have to turn one down.
I made a list of the ones I wanted to apply to, when the application open and close. I have downloaded the templates and slowly working through them. I presume if your applying for a postdoc you will need a PI support ask them how they feel. Also, look at your uni guidelines, in mine, they have to approve all grant applications and arent ken on people applying with the same proposal over and over again, I have to change them up.