For multiple records you put placeholders for 1 instance on the template. ID adds the others acording to the spacing you define. The less obvious problem is that EVERYTHING on the page is duplicated, so the calculations are based on the bounding box that surrounds all the page items (my recollection is that this is true when you set up on the document page, but if you use the master page only objects containing fields or grouped with objects containing fields will be duplicated) so you have to be sure there are no extra frames (like headers or footers, for example), and that you've reduced frames to the minimum required sizes to hold your data, or there simply may not be room on the page to hold more than one copy of everything.
please tell me what you mean by "defining space". I am working on an A5 sized page. and i have assigned place holders for ONE record. i had previously used a footer (defined on the master page) which i removed - but i am still getting only one record per page. the records are small enough - 3 should atleast fit in one page.
If you were to select EVERYTHING on the page, could you copy it and paste a second copy of it outside the bounding box of what you selected, and still keep it ALL inside the page? For example if you have a text frame that is tall, but the fields are only at the top, it isn't the area that is consumed by what you see that counts, it's the height of the frame, and if you can't stack more than one, then you won't get multiple records.
this issue comes up regularly in this forum.
if the OP is talking about putting records in the same text frame, that won't work as there's no "next record" feature like there is in MS word.
yes, indesign can do multiple records per page but it does this by replicating the objects on a page based from the top-left most object to the bottom-right object, so if the text box goes to the end of the page then there is literally no room to put another record on that page.
i've done a piece on my own blog about the pitfalls of data merge:
look at point six of the story - it is effectively what peter has been saying.