When notified of a multiple offer(s) you have an opportunity to revise the offer, should you choose to do so, provided you can meet the timelines they set for presentation.

As a general rule, it’s a good idea to make your best offer in these circumstances, as you may not get a second chance. Things the seller might consider are; if they have a preference in completion dates, the offer price, the deposit amounts, and what conditions (if any), and how long the due diligence period is for.

With the offer price, only you know how much the property means to you, and what is the most you are willing to pay. It’s important to consider and understand that if it sold for even a slightly greater amount than you offered, it was beyond what you were willing to pay.
Be aware that even a full-price offer or better than a full price offer does not guarantee your purchase of the property - other offers may be for above the asking price or may have less or no conditions. The seller is not obligated to “sell” their home even if the offer is unconditional and full price.
A property is worth what someone is willing to pay for it. As a buyer you need to put yourself in the position that you will have no regrets if someone else gets it, knowing you put your best offer forward. Knowing what to offer and being confident in your offer price makes the process less stressful.

Some sellers will see a large deposit as a stronger offer.
Considering paying the deposit in a quick timeframe and with certified funds – this can reassure the seller of your intent and may set you apart from other offers.

Conditions Precedent/Due Diligence
The strength of your offer is not based on price alone. You need to seriously consider the value of having those conditions, versus making your offer firm and binding upon acceptance by the seller. If conditions are even accepted in a multiple offer situation, they need to be minimal and removed sooner rather than later. You may want to consider consulting with the service providers you will engage to do your due diligence, and finding out when the next available spots are, or consider “booking/holding” dates, depending on cancellation policies. If timing and the seller allows, prior to offers being presented, you could consider a pre-inspection risking that you may spend funds on due diligence without getting the home.
If time allows, prior to the presentation of offers, you may want to consider seeking permission of the seller, to do the due diligence in advance, with the understanding that you may be investing monies into the due diligence, without the assurance that your offer will be successful.
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With the due diligence, remember if these are NOT listed as conditions, you will not have the ability to do them prior to purchase. There is a risk that should be considered in not doing due diligence, (i.e., if items are discovered at a later date), unless the seller didn’t disclose a material latent defect that they were aware of and you can prove the same – there may be no recourse.

Completion Dates
Timing matters with closing dates and these can have a huge impact. As such, if you have flexibility, you may wish to consider asking the seller as to their preferred completion dates.

When you are in a multiple offer situation as a buyer, you might want to consider leaving out that extra fridge, or whatever else you were hoping would be thrown into the deal.

Offer Open for Acceptance
The period given with an offer (the time a seller has to accept the offer as delivered) can also play an enormous part in the way a multiple offer situation is handled.
However, pressing a seller to respond quickly can backfire on you, or, with the right dollar amount, can put you ahead of the competition.

The Personal Touch
There are many tactics being used by home buyers to stand out from the crowd. While not all sellers will read them, personalized letters are the most-accepted and popular form of unique buyer strategies available.
So, there are a LOT of considerations. In multiple offers situations there is one lucky buyer who has the opportunity to buy the property.

Additional Info
Offers are normally presented to the seller in the order they were received. It's very important to remember that under most circumstances the seller is under no obligation to consider, respond, or counter your offer. Just because it may have been the first offer presented does not mean the seller is obliged to consider it, and respond to it, prior to considering and dealing with other offers.
The seller may have given instructions to the listing agent not to divulge to the REALTORS® acting for potential buyers that multiple offers exist – therefore, other offers may exist that you are not aware of.
Unless you enter into a “confidentiality” agreement, prior to submitting your offer, the seller may share details of your offer with other buyers.

Source: BCREA