I am currently an intern for a large (non tech) company working in a technical role. I will graduate in about six months. I have been applying to a number of full time roles with businesses that better align to my personal career goals and interests. To date, I have not heard back from any of the jobs I have applied to, but it has been less than a month, and with six months until graduation I feel that may not mean much. I feel I am well qualified for the jobs I have applied for, and therefore have a fairly good chance of receiving an offer from one of them.
To make matters difficult, however, I have just been offered a full time role with the company I am doing my internship with, to start after graduation. This role does not closely align with my professional or career goals, and I believe I could get better compensation elsewhere. The deadline for accepting this offer is about 2-3 weeks from now.
I don't want to turn down what, in the end, is really not a bad offer, but I don't know when I could expect a decision from the companies I am more interested in.
I believe this situation is slightly different than others posted on the site in that the offer I have on the table now was not for an advertised, open position I applied for, but rather one that was extended only because they liked my work as an intern. Furthermore, the companies in question are in no way competitors (one is a financial institution and the other a technology firm). How do I deal with this situation if the company in question refuses to extend their decision deadline?
EDIT for clarification:
If I do not accept the offer I do not believe they are actively looking for someone else.
The internship started 10 months ago and will continue until I graduate. The company has no influence on my graduation,