My vector eps that I purchased has a white background that I don't want when I bring it into InDesign. I do not want to change it to a jpeg because I want to be able to enlarge the image quite a bit and keep the quality.
The first step is to verify the white isn't actually part of the artwork. To do this you need to open the EPS in a vector editor - Illustrator or Inkscape. Then check the construction.
If there's a white object for the background, merely remove it and resave the file.
If there is no white object for the background... Some applications, when saving an EPS, have options to add a background. So, to overcome that, you merely need to resave the file.
Because you are using Indesign, I would open and resave the file (using
Save As) as an .ai file.
The .ai file will still be vector if the eps was vector. The artwork won't change in any way. What does change is the "wrapper" the artwork is contained in. EPS is merely a file wrapper and like all wrappers has some limitations. Because you are using InDesign, using the .ai format will actually provide you with a bit more options when importing the artwork. And if the background was part of the "EPS wrapper", the resaving will remove that background.