I have accepted the first company’s offer, and it has filed for my H1B transfer. Now, I want to sign an offer from Company two and potentially join it. So, should I make the company speed up the process and delay joining the company in order not to get issues during the green card process? What if the company forces me to join?
You can file multiple H-1B transfers simultaneously, and it's legal. Approval of one transfer doesn’t obligate you to join that employer, nor does it affect your existing H-1B status with your current employer. You can choose to join any employer whose transfer gets approved, provided all transfers were filed while you were in valid status with your current employer.
However, if your H-1B validity is close to expiring (e.g., within 6 months), later-filed transfers may require "bridge petitions" to maintain continuity of status. Consult an immigration lawyer to ensure proper handling and avoid complications.