Great question! You totally can.
The verb 서다 describes not only a change in the state of something (changing from sitting to standing) but also as a persisted state (standing). This causes slight changes in meaning when trying to describe an ongoing action/state.
여자가 서고 있어요 = "A woman is standing (up)." (The woman is in the middle/in the process of standing up from a seated position.)
여자가 서 있어요 = "A woman is standing." (The woman has already changed her position to "standing" and continues to stand.)
There are two ways in Korean to form something like the continuous tense in English. As a rule of thumb, the ~고 있다 grammar emphasizes the ongoing action, while the ~아/어 있다 grammar emphasizes the ongoing state after an action.
• 서고 있다, be getting to the "standing" position is a movement verb. The process is so brief that this form is only used if one wishes to be specific.
여자가 서고 있다 => The woman is on the verge of getting up on her feet
• 서 있다, be standing (i.e. be in the standing position /be on one's feet) is a stasis verb describing a posture.
여자가 서 있다 = The woman is standing (/is currently on her feet).
This distinction between progression (movement) and procession (stasis) can be found in all Korean posture verbs 서다 (to stand); 앉다 (to sit); 눕다 (to lie down) ...
Thinking definition [...] If you describe someone as a thinking man or woman, you mean that they are intelligent and take an interest in important events and issues, and you approve of this. Syn: thoughtful, intelligent, cultured...
A thinking woman (she-thinker) is standing = "여성 사상가가 서 있어요"
"생각하는 여자가 서 있어요." simply means a woman (who is) in thought is standing
As for A woman is standing thinking, this may be construed as she is "standing and thinking", 여자가 서서 생각하고 있어요.