This is a fantastic question. First of all, I apologize for the late answer - I was away this weekend, and then needed to consult my sources. With that said, here it goes.

The short answer to this is yes, buyers of a custom-made armour in the 15th century absolutely could select 'options' when discussing their armour with the armourer that would make it. As the armourer Martin Rondelle of Bruges bragged to John Paston (of East Anglia in England) in 1473:

..Moreover, I have heard that you would like to have a full armour. As I recently took your measurements when you were in this town of Bruges, you know that I still have them for all pieces. For this reason, if you would like me to make it for you, I will do it willingly and all the elements that you would like made. With regard to the price, I shall ensure that you shall be satisfied with me. So, when you know what pieces you would like to have and the style and the day you would like to receive them through someone with whom I can deal in your name and who will pay me a deposit, I will work so well that, God willing, you will praise me.

Now, first of all this letter is a great piece of salesmanship. But a good salesman doesn't promise more than he can deliver, especially when the final payment will be received on receipt of the finished product! So it is telling that Rondelle offers Paston his choice of both 'pieces' (IE, what individual pieces of armour he would like) and the overall 'style.' Since Paston is in the market for a full armour, the choice of pieces may refer to choosing between options for the armour's elements, such as between a Sallet and an armet for the helmet. 'Style' here probably refers to the the decorative scheme (fluted versus not, applied brass borders or not, the patterns to stamp on those borders), but it can also refer to a more fundamental question of construction - how long the skirt is (long in the English fashion, shorter in the neatherlandish/flemish/French/Italian fashion), what the construction of the guantlets is (mitten, half-mitten, fingered), how the pauldrons/spaulders are constructed. Importantly, this is an international order, being ordered by a man in a country that had both its own native armour style and a variety of foreign influences, and being ordered from a man who was in a country with a combination of native and Italian armourers. Both Paston and Rondelle would be acquainted with a variety of armour styles.

We have other examples. In 1438 the Duke of Burgundy ordered gauntlets in 'The English Fashion' - specifically requesting a distinctive, foreign style for his own gauntlets. Orders for armour (even mass orders) often specify the helmet type, sallet - armet, etc. The type of helmet was not merely assumed.

We also have surviving armours that appear to show stylistic elements of their buyer's country, not of their maker's country. A dramatic example is the 'Export' armours of Brescia and Milan, which were fluted (in a way that Milanese armours weren't). Even more extreme, the armours 'alla tedesca' of the late 15th century look very nearly like later 15th century 'Gothic' armours from Southern Germany.

In at least one example we find a maker of 'classic' Milanese armour adapting his work to a foreign client. Tomaso Missaglia is from the most famous family of Milanese armourers in the 15th century - not just armourers, they were merchant/capitalists (industrialists, almost) whose commercial interests included branches in multiple European Countries and multiple Italian cities as well as mutliple workshops in Milan. Collectors value their work as an examplar of the 15th century Milanese style see a late example here. Elements of this style include armet helmets, asymmetrical pauldrons, and asymmetrical arm defenses (features a heavy elbow guard on the left arm, the gaurd of the vambrace). However, in the Kunsthistorichesmuseum in Vienna we see the armour of Friedrich of Pflaz, Count Palatine of the Rhine. Note its design - symmetrical spaulders with besagews, a great bascinet (of the sort that Italians had never worn much), and symmetrical vambraces. Now, this armour is still identifiably 'Italian' in make - we see a high lance rest attachment via a pin-and-staple, vambraces rivetted together at the elbow (rather than being made in 3 parts), a strapped plackart (lower breastplate) and other features. So what we see is an armourer working within some basic assumptions of how armour is put together (which he takes from his training) mixing and matching elements for his client. And this is how armourers worked generally - they had basic construction elements that they took from their training, but they were able to adapt the details to the needs of the client.

Now, it should be said that this flexibility is much more likely from centers of armour production that served international markets, or were part of a large cross-cultural exchange. I detect less 'borrowing' and adaptation in the works of south German armourers in the 'high gothic' period (which was not very long, c.1460-1485, but which is famous due to the beauty of the armours produced). But then, at this time Augsburg was not the international armouring center it would become as the power of its Habsburg patrons expanded across Europe.

In the 16th century we have even more evidence of how armour was bought. We have pattern books, which could be used to select designs for decoration and armour designs. We also have corpus's of armours that seem to show the stylistic preferences of the purchaser - for instance, Charles V's armours all begin to feature the Virgin Mary prominently on the breastplate in the 1530's, around the time his struggles against both North African 'Moorish' powers and reforming 'heretics' in Germany were intensifying. He also seems to have a fondness for parellel or radiating bands of gold, often sunken into the armour - a feature seen on other 16th century German armours, but not nearly as much as on Charles'. Beyond this, we have a wealth of documentary evidence of how armour was bought, and what people specified when buying it.

To conclude, when you comissioned an armour to be made for your, customization was one of the perks you were buying with all that extra money (at least several times the cost of an 'off the rack' or used harness). And it should be remembered that truly custom armour was the privelege of the elite of the elite - the upper echelons of the military aristocracy and royalty. Most fully armoured men at arms (people who were in the wealthier portion of society already) wold wear armour bought 'off the rack' or perhaps used, whether they were buying it themselves or whether it was bought for them by wealthier employers or patrons. This was not the cruder 'munition' armour worn by infantrymen - it was full armour, constructed like any 'knightly' armour, but without either the fit or the finish (or the customization options) offered by a bespoke armourer. It is like the differences between a perfectly fine suit purchased at a department store and a bespoke suit from Saville Row. To extend the metaphor, munition armour would be like khakis and a polo from Target.

Sources:

Matthais Pfaffenbichler - Armourers

Tobias Capwell - Armour of the English Knight 1400-1450

Nickolas Dupras - Armourers and their Workshops