"possibilities for interpretation" is a correct and usable phrase in written English.
You can use the phrase when you are referring to a range of potential interpretations or understandings of something. For example, "By presenting the information in this way, I hope to leave open a variety of possibilities for interpretation."
"But to me, everyday reality presents infinite possibilities for interpretation.
"The movements generate a tension between the planned and the accidental, with each new variation opening up possibilities for interpretation.
But should you not care for the man-and-tiger survival struggle told in one way on one level, there are infinite possibilities for interpretation of life's universal truths, as Pi himself summarizes by saying, "And so it goes with God".
The difference in the results across studies raises several possibilities for interpretation.
The results of this study allow increasing the possibilities for interpretation of two generic HRQL questionnaires in future studies where the questionnaires are applied.
The translations, culled from many different sources--from professional translators and native speakers, to online translation services--show the range of possibility for interpretation, including sometimes poetic, or less than poetic, mis-interpretation.
However, included studies were heterogeneous regarding conduction and interpretation of TEG/ROTEM, and no studies reported whether results of TEG/ROTEM were interpreted with or without knowledge of the used reference test, which leaves the possibility for interpretation bias.
It gives the student of world religions a valuable sense of perspective, and the student of dreams a glimpse at the rich possibilities for dream interpretation.
Social dilemmas provide intriguing possibilities for the interpretation of QS phenomena [20], [21], [22].
So filled with possibilities for metaphorical interpretation, the term has been widely used, most famously in regards to multiculturalism.
Moreover, without parentheses, this phrase would sound too futile and deterministic; broken down into two parts, ground-less embraces possibilities for multiple interpretations.
